Einstein Constraints And Ricci Flow

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Einstein Constraints and Ricci Flow

Author : Mauro Carfora
Publisher : Springer Nature
ISBN 13 : 9811985405
Total Pages : 181 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Einstein Constraints and Ricci Flow by : Mauro Carfora

Download or read book Einstein Constraints and Ricci Flow written by Mauro Carfora and published by Springer Nature. This book was released on 2023-01-10 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.

The Ricci Flow

Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Ricci Flow by :

Download or read book The Ricci Flow written by and published by . This book was released on 2007 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on the Ricci Flow

Author : Peter Topping
Publisher : Cambridge University Press
ISBN 13 : 0521689473
Total Pages : 124 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Lectures on the Ricci Flow by : Peter Topping

Download or read book Lectures on the Ricci Flow written by Peter Topping and published by Cambridge University Press. This book was released on 2006-10-12 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to Ricci flow suitable for graduate students and research mathematicians.

Space – Time – Matter

Author : Jochen Brüning
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110452154
Total Pages : 518 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Space – Time – Matter by : Jochen Brüning

Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

The Ricci Flow: Techniques and Applications

Author : Bennett Chow
Publisher : American Mathematical Soc.
ISBN 13 : 0821844296
Total Pages : 489 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Ricci Flow: Techniques and Applications by : Bennett Chow

Download or read book The Ricci Flow: Techniques and Applications written by Bennett Chow and published by American Mathematical Soc.. This book was released on 2007 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ricci Flow

Author : Bennett Chow
Publisher :
ISBN 13 : 9781470426774
Total Pages : pages
Book Rating : 4.4/5 (267 download)

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Book Synopsis Ricci Flow by : Bennett Chow

Download or read book Ricci Flow written by Bennett Chow and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Poincare Conjecture

Author : James Carlson
Publisher : American Mathematical Soc.
ISBN 13 : 0821898655
Total Pages : 185 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Poincare Conjecture by : James Carlson

Download or read book The Poincare Conjecture written by James Carlson and published by American Mathematical Soc.. This book was released on 2014-10-16 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conference to celebrate the resolution of the Poincare conjecture, which is one of the Clay Mathematics Institute's seven Millennium Prize Problems, was held at the Institut Henri Poincare in Paris. Several leading mathematicians gave lectures providing an overview of the conjecture--its history, its influence on the development of mathematics, and, finally, its proof. This volume contains papers based on the lectures at that conference. Taken together, they form an extraordinary record of the work that went into the solution of one of the great problems of mathematics.

The Fifth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories

Download The Fifth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories PDF Online Free

Author : D. G. Blair
Publisher :
ISBN 13 :
Total Pages : 1224 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis The Fifth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories by : D. G. Blair

Download or read book The Fifth Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories written by D. G. Blair and published by . This book was released on 1989 with total page 1224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inspired By S S Chern: A Memorial Volume In Honor Of A Great Mathematician

Author : Phillip A Griffiths
Publisher : World Scientific
ISBN 13 : 9814476846
Total Pages : 532 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Inspired By S S Chern: A Memorial Volume In Honor Of A Great Mathematician by : Phillip A Griffiths

Download or read book Inspired By S S Chern: A Memorial Volume In Honor Of A Great Mathematician written by Phillip A Griffiths and published by World Scientific. This book was released on 2006-11-27 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shiing-Shen Chern (1911-2004) was one of the leading differential geometers of the twentieth century. In 1946, he founded the Mathematical Institute of Academia Sinica in Shanghai, which was later moved to Nanking. In 1981, he founded the Mathematical Sciences Research Institute (MSRI) at Berkeley and acted as the director until 1984. In 1985, he founded the Nankai Institute of Mathematics in Tianjin. He was awarded the National Medal of Science in 1975; the Wolf Prize in mathematics in 1984; and the Shaw Prize in mathematical sciences in 2004.Chern's works span all the classic fields of differential geometry: the Chern-Simons theory; the Chern-Weil theory, linking curvature invariants to characteristic classes; Chern classes; and other areas such as projective differential geometry and webs that are mathematically rich but currently have a lower profile. He also published work in integral geometry, value distribution theory of holomorphic functions, and minimal submanifolds.Inspired by Chern and his work, former colleagues, students and friends — themselves highly regarded mathematicians in their own right — come together to honor and celebrate Chern's huge contributions. The volume, organized by Phillip Griffiths of the Institute for Advanced Study (Princeton), contains contributions by Michael Atiyah (University of Edinburgh), C-M Bai (Nankai), Robert Bryant (Duke University), Kung-Ching Chang (Peking University), Jeff Cheeger (New York University), Simon K Donaldson (Imperial College), Hélène Esnault (Universität Duisburg-Essen), Mo-Lin Ge (Nankai), Mark Green (University of California at Los Angeles), Phillip Griffiths (Institute for Advanced Study), F Reese Harvey (Rice University), Alain Hénaut (Université Bordeaux 1), Niky Kamran (McGill University), Bruce Kleiner (Yale), H Blaine Lawson, Jr (Suny at Stony Brook), Yiming Long (Nankai), Xiaonan Ma (UMR 7640 du CNRS), Luc Pirio (IRMAR, France), Graeme Segal (Oxford), Gang Tian (MIT), Jean-Marie Trepreau (Institut de Mathématiques de Jussieu), Jeff Viaclovsky (MIT), Wei Wang (Nankai), Wentsun Wu (Chinese Academy of Sciences), C N Yang (Tsinghua), Tan Zhang (Murray State University), Weiping Zhang (Nankai) and others.

Hamilton’s Ricci Flow

Author : Bennett Chow
Publisher : American Mathematical Society, Science Press
ISBN 13 : 1470473690
Total Pages : 648 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hamilton’s Ricci Flow by : Bennett Chow

Download or read book Hamilton’s Ricci Flow written by Bennett Chow and published by American Mathematical Society, Science Press. This book was released on 2023-07-13 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ricci flow is a powerful analytic method for studying the geometry and topology of manifolds. This book is an introduction to Ricci flow for graduate students and mathematicians interested in working in the subject. To this end, the first chapter is a review of the relevant basics of Riemannian geometry. For the benefit of the student, the text includes a number of exercises of varying difficulty. The book also provides brief introductions to some general methods of geometric analysis and other geometric flows. Comparisons are made between the Ricci flow and the linear heat equation, mean curvature flow, and other geometric evolution equations whenever possible. Several topics of Hamilton's program are covered, such as short time existence, Harnack inequalities, Ricci solitons, Perelman's no local collapsing theorem, singularity analysis, and ancient solutions. A major direction in Ricci flow, via Hamilton's and Perelman's works, is the use of Ricci flow as an approach to solving the Poincaré conjecture and Thurston's geometrization conjecture.

The Ricci Flow: An Introduction

Author : Bennett Chow
Publisher : American Mathematical Soc.
ISBN 13 : 0821835157
Total Pages : 342 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Ricci Flow: An Introduction by : Bennett Chow

Download or read book The Ricci Flow: An Introduction written by Bennett Chow and published by American Mathematical Soc.. This book was released on 2004 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ricci flow is a powerful technique that integrates geometry, topology, and analysis. Intuitively, the idea is to set up a PDE that evolves a metric according to its Ricci curvature. The resulting equation has much in common with the heat equation, which tends to 'flow' a given function to ever nicer functions. By analogy, the Ricci flow evolves an initial metric into improved metrics. Richard Hamilton began the systematic use of the Ricci flow in the early 1980s and applied it in particular to study 3-manifolds. Grisha Perelman has made recent breakthroughs aimed at completing Hamilton's program. The Ricci flow method is now central to our understanding of the geometry and topology of manifolds.This book is an introduction to that program and to its connection to Thurston's geometrization conjecture. The authors also provide a 'Guide for the hurried reader', to help readers wishing to develop, as efficiently as possible, a nontechnical appreciation of the Ricci flow program for 3-manifolds, i.e., the so-called 'fast track'. The book is suitable for geometers and others who are interested in the use of geometric analysis to study the structure of manifolds. "The Ricci Flow" was nominated for the 2005 Robert W. Hamilton Book Award, which is the highest honor of literary achievement given to published authors at the University of Texas at Austin.

Comparison Geometry

Author : Karsten Grove
Publisher : Cambridge University Press
ISBN 13 : 9780521592222
Total Pages : 280 pages
Book Rating : 4.5/5 (922 download)

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Book Synopsis Comparison Geometry by : Karsten Grove

Download or read book Comparison Geometry written by Karsten Grove and published by Cambridge University Press. This book was released on 1997-05-13 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an up to date work on a branch of Riemannian geometry called Comparison Geometry.

The Ricci flow

Author : Bennett Chow
Publisher :
ISBN 13 : 9780012946381
Total Pages : 325 pages
Book Rating : 4.9/5 (463 download)

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Book Synopsis The Ricci flow by : Bennett Chow

Download or read book The Ricci flow written by Bennett Chow and published by . This book was released on 2004 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Ricci Flow: Analyic aspects

Author :
Publisher :
ISBN 13 : 9780821839461
Total Pages : pages
Book Rating : 4.8/5 (394 download)

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Book Synopsis The Ricci Flow: Analyic aspects by :

Download or read book The Ricci Flow: Analyic aspects written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Emergence Theme of Physics

Author : Robert Carroll
Publisher : World Scientific
ISBN 13 : 9814291803
Total Pages : 288 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis On the Emergence Theme of Physics by : Robert Carroll

Download or read book On the Emergence Theme of Physics written by Robert Carroll and published by World Scientific. This book was released on 2010 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.

The Ricci Flow: Analytic aspects

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (123 download)

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Book Synopsis The Ricci Flow: Analytic aspects by :

Download or read book The Ricci Flow: Analytic aspects written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Einstein Equations and the Large Scale Behavior of Gravitational Fields

Author : Piotr T. Chrusciel
Publisher : Birkhäuser
ISBN 13 : 3034879539
Total Pages : 487 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Einstein Equations and the Large Scale Behavior of Gravitational Fields by : Piotr T. Chrusciel

Download or read book The Einstein Equations and the Large Scale Behavior of Gravitational Fields written by Piotr T. Chrusciel and published by Birkhäuser. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.