Recent Progress In Conformal Geometry

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Recent Progress In Conformal Geometry

Author : Abbas Bahri
Publisher : World Scientific
ISBN 13 : 1908979313
Total Pages : 522 pages
Book Rating : 4.9/5 (89 download)

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Book Synopsis Recent Progress In Conformal Geometry by : Abbas Bahri

Download or read book Recent Progress In Conformal Geometry written by Abbas Bahri and published by World Scientific. This book was released on 2007-04-05 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction.In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form, and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces, therefore, a practical tool in the field, and this homology becomes computable./a

Recent Progress in Conformal Geometry

Author : Abbas Bahri
Publisher : World Scientific
ISBN 13 : 1860947727
Total Pages : 522 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Recent Progress in Conformal Geometry by : Abbas Bahri

Download or read book Recent Progress in Conformal Geometry written by Abbas Bahri and published by World Scientific. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction.In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form, and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces, therefore, a practical tool in the field, and this homology becomes computable.

Conformal Groups in Geometry and Spin Structures

Author : Pierre Anglès
Publisher : Springer Science & Business Media
ISBN 13 : 0817646434
Total Pages : 307 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Conformal Groups in Geometry and Spin Structures by : Pierre Anglès

Download or read book Conformal Groups in Geometry and Spin Structures written by Pierre Anglès and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.

Locally Conformal Kähler Geometry

Author : Sorin Dragomir
Publisher : Springer Science & Business Media
ISBN 13 : 1461220262
Total Pages : 332 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Locally Conformal Kähler Geometry by : Sorin Dragomir

Download or read book Locally Conformal Kähler Geometry written by Sorin Dragomir and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: . E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

Conformal Geometry and Quasiregular Mappings

Author : Matti Vuorinen
Publisher :
ISBN 13 : 9783662192122
Total Pages : 236 pages
Book Rating : 4.1/5 (921 download)

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Book Synopsis Conformal Geometry and Quasiregular Mappings by : Matti Vuorinen

Download or read book Conformal Geometry and Quasiregular Mappings written by Matti Vuorinen and published by . This book was released on 2014-01-15 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Developments in Pseudo-Riemannian Geometry

Author : Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher : European Mathematical Society
ISBN 13 : 9783037190517
Total Pages : 556 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Recent Developments in Pseudo-Riemannian Geometry by : Dmitriĭ Vladimirovich Alekseevskiĭ

Download or read book Recent Developments in Pseudo-Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and published by European Mathematical Society. This book was released on 2008 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.

Two-Dimensional Conformal Geometry and Vertex Operator Algebras

Author : Yi-Zhi Huang
Publisher : Springer Science & Business Media
ISBN 13 : 1461242762
Total Pages : 289 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Two-Dimensional Conformal Geometry and Vertex Operator Algebras by : Yi-Zhi Huang

Download or read book Two-Dimensional Conformal Geometry and Vertex Operator Algebras written by Yi-Zhi Huang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Boyan Sirakov
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5393 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Boyan Sirakov and published by World Scientific. This book was released on 2019-02-27 with total page 5393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Topological, Differential and Conformal Geometry of Surfaces

Author : Norbert A'Campo
Publisher : Springer Nature
ISBN 13 : 3030890325
Total Pages : 282 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Topological, Differential and Conformal Geometry of Surfaces by : Norbert A'Campo

Download or read book Topological, Differential and Conformal Geometry of Surfaces written by Norbert A'Campo and published by Springer Nature. This book was released on 2021-10-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.

Recent Developments in Quantum Affine Algebras and Related Topics

Author : Naihuan Jing
Publisher : American Mathematical Soc.
ISBN 13 : 0821811991
Total Pages : 482 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Quantum Affine Algebras and Related Topics by : Naihuan Jing

Download or read book Recent Developments in Quantum Affine Algebras and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 1999 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Perspectives in Nonlinear Partial Differential Equations

Author : Henri Berestycki
Publisher : American Mathematical Soc.
ISBN 13 : 0821841904
Total Pages : 522 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Perspectives in Nonlinear Partial Differential Equations by : Henri Berestycki

Download or read book Perspectives in Nonlinear Partial Differential Equations written by Henri Berestycki and published by American Mathematical Soc.. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: In celebration of Haim Brezis's 60th birthday, a conference was held at the Ecole Polytechnique in Paris, with a program testifying to Brezis's wide-ranging influence on nonlinear analysis and partial differential equations. The articles in this volume are primarily from that conference. They present a rare view of the state of the art of many aspects of nonlinear PDEs, as well as describe new directions that are being opened up in this field. The articles, written by mathematicians at the center of current developments, provide somewhat more personal views of the important developments and challenges.

Fourteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg14 Meeting On General Relativity (In 4 Parts)

Download Fourteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg14 Meeting On General Relativity (In 4 Parts) PDF Online Free

Author : Massimo Bianchi
Publisher : World Scientific
ISBN 13 : 9813226617
Total Pages : 4784 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Fourteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg14 Meeting On General Relativity (In 4 Parts) by : Massimo Bianchi

Download or read book Fourteenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical And Experimental General Relativity, Astrophysics, And Relativistic Field Theories - Proceedings Of The Mg14 Meeting On General Relativity (In 4 Parts) written by Massimo Bianchi and published by World Scientific. This book was released on 2017-10-13 with total page 4784 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four volumes of the proceedings of MG14 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 35 morning plenary talks over 6 days, 6 evening popular talks and 100 parallel sessions on 84 topics over 4 afternoons.Volume A contains plenary and review talks ranging from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics.The remaining volumes include parallel sessions which touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity.

Integro-Differential Elliptic Equations

Author : Xavier Fernández-Real
Publisher : Springer Nature
ISBN 13 : 3031542428
Total Pages : 409 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Integro-Differential Elliptic Equations by : Xavier Fernández-Real

Download or read book Integro-Differential Elliptic Equations written by Xavier Fernández-Real and published by Springer Nature. This book was released on 2024 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters

Recent Advances in Nonlinear Partial Differential Equations and Applications

Author : Luis López Bonilla
Publisher : American Mathematical Soc.
ISBN 13 : 0821842110
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Advances in Nonlinear Partial Differential Equations and Applications by : Luis López Bonilla

Download or read book Recent Advances in Nonlinear Partial Differential Equations and Applications written by Luis López Bonilla and published by American Mathematical Soc.. This book was released on 2007 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles of this book are written by leading experts in partial differential equations and their applications, who present overviews here of recent advances in this broad area of mathematics. The formation of shocks in fluids, modern numerical computation of turbulence, the breaking of the Einstein equations in a vacuum, the dynamics of defects in crystals, effects due to entropy in hyperbolic conservation laws, the Navier-Stokes and other limits of the Boltzmann equation, occupancy times for Brownian motion in a two dimensional wedge, and new methods of analyzing and solving integrable systems are some of this volume's subjects. The reader will find an exposition of important advances without a lot of technicalities and with an emphasis on the basic ideas of this field.

Non-linear Elliptic Equations in Conformal Geometry

Author : Sun-Yung A. Chang
Publisher : European Mathematical Society
ISBN 13 : 9783037190067
Total Pages : 106 pages
Book Rating : 4.1/5 (9 download)

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Book Synopsis Non-linear Elliptic Equations in Conformal Geometry by : Sun-Yung A. Chang

Download or read book Non-linear Elliptic Equations in Conformal Geometry written by Sun-Yung A. Chang and published by European Mathematical Society. This book was released on 2004 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian. In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g., higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four. The material is suitable for graduate students and research mathematicians interested in geometry, topology, and differential equations.

Mathematics of Surfaces XIII

Author : Edwin R. Hancock
Publisher : Springer
ISBN 13 : 3642035965
Total Pages : 418 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Mathematics of Surfaces XIII by : Edwin R. Hancock

Download or read book Mathematics of Surfaces XIII written by Edwin R. Hancock and published by Springer. This book was released on 2009-08-27 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th IMA International Conference on the Mathematics of Surfaces held in York, UK in September 2009. The papers in the present volume include seven invited papers, as well as 16 submitted papers. The topics covered include subdivision schemes and their continuity, polar patchworks, compressive algorithms for PDEs, surface invariant functions, swept volume parameterization, Willmore flow, computational conformal geometry, heat kernel embeddings, and self-organizing maps on manifolds, mesh and manifold construction, editing, flattening, morphing and interrogation, dissection of planar shapes, symmetry processing, morphable models, computation of isophotes, point membership classification and vertex blends. Surface types considered encompass polygon meshes as well as parametric and implicit surfaces.

A Short Course in Computational Geometry and Topology

Author : Herbert Edelsbrunner
Publisher : Springer Science & Business
ISBN 13 : 3319059572
Total Pages : 105 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis A Short Course in Computational Geometry and Topology by : Herbert Edelsbrunner

Download or read book A Short Course in Computational Geometry and Topology written by Herbert Edelsbrunner and published by Springer Science & Business. This book was released on 2014-04-28 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.