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Maximum Principles On Riemannian Manifolds And Applications
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Book Synopsis Maximum Principles on Riemannian Manifolds and Applications by : Stefano Pigola
Download or read book Maximum Principles on Riemannian Manifolds and Applications written by Stefano Pigola and published by American Mathematical Soc.. This book was released on 2005 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to introduce the reader to various forms of the maximum principle, starting from its classical formulation up to generalizations of the Omori-Yau maximum principle at infinity obtained by the authors.
Book Synopsis Maximum Principles and Geometric Applications by : Luis J. Alías
Download or read book Maximum Principles and Geometric Applications written by Luis J. Alías and published by Springer. This book was released on 2016-02-13 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to some geometric and analytic aspects of the maximum principle. In doing so, it analyses with great detail the mathematical tools and geometric foundations needed to develop the various new forms that are presented in the first chapters of the book. In particular, a generalization of the Omori-Yau maximum principle to a wide class of differential operators is given, as well as a corresponding weak maximum principle and its equivalent open form and parabolicity as a special stronger formulation of the latter. In the second part, the attention focuses on a wide range of applications, mainly to geometric problems, but also on some analytic (especially PDEs) questions including: the geometry of submanifolds, hypersurfaces in Riemannian and Lorentzian targets, Ricci solitons, Liouville theorems, uniqueness of solutions of Lichnerowicz-type PDEs and so on. Maximum Principles and Geometric Applications is written in an easy style making it accessible to beginners. The reader is guided with a detailed presentation of some topics of Riemannian geometry that are usually not covered in textbooks. Furthermore, many of the results and even proofs of known results are new and lead to the frontiers of a contemporary and active field of research.
Book Synopsis Uncertainty Principles on Riemannian Manifolds by : Wolfgang Erb
Download or read book Uncertainty Principles on Riemannian Manifolds written by Wolfgang Erb and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, the Heisenberg-Pauli-Weyl uncertainty principle on the real line and the Breitenberger uncertainty on the unit circle are generalized to Riemannian manifolds. The proof of these generalized uncertainty principles is based on an operator theoretic approach involving the commutator of two operators on a Hilbert space. As a momentum operator, a special differential-difference operator is constructed which plays the role of a generalized root of the radial part of the Laplace-Beltrami operator. Further, it is shown that the resulting uncertainty inequalities are sharp. In the final part of the thesis, these uncertainty principles are used to analyze the space-frequency behavior of polynomial kernels on compact symmetric spaces and to construct polynomials that are optimally localized in space with respect to the position variance of the uncertainty principle.
Book Synopsis A geometric maximum principle for surfaces of prescribed mean curvature in Riemannian manifolds by : Ulrich Dierkes
Download or read book A geometric maximum principle for surfaces of prescribed mean curvature in Riemannian manifolds written by Ulrich Dierkes and published by . This book was released on 1986 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Classification Theory of Riemannian Manifolds by : S. R. Sario
Download or read book Classification Theory of Riemannian Manifolds written by S. R. Sario and published by Springer. This book was released on 2006-11-15 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum and Comparison Principles at Infinity on Riemannian Manifolds by : Stefano Pigola
Download or read book Maximum and Comparison Principles at Infinity on Riemannian Manifolds written by Stefano Pigola and published by . This book was released on 2003 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential and Riemannian Manifolds by : Serge Lang
Download or read book Differential and Riemannian Manifolds written by Serge Lang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).
Download or read book Manifolds II written by Paul Bracken and published by BoD – Books on Demand. This book was released on 2019-05-22 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry is a very active field of research and has many applications to areas such as physics, in particular gravity. The chapters in this book cover a number of subjects that will be of interest to workers in these areas. It is hoped that these chapters will be able to provide a useful resource for researchers with regard to current fields of research in this important area.
Book Synopsis Harmonic Mappings Between Riemannian Manifolds by : Jürgen Jost
Download or read book Harmonic Mappings Between Riemannian Manifolds written by Jürgen Jost and published by . This book was released on 1984 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 by : Takuro Mochizuki
Download or read book Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2 written by Takuro Mochizuki and published by American Mathematical Soc.. This book was released on 2007 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regularholonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Book Synopsis Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 by : Takuro Mochizuki
Download or read book Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 written by Takuro Mochizuki and published by American Mathematical Soc.. This book was released on 2007 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As another application, the author establishes the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.
Book Synopsis Geometric Methods in PDE’s by : Giovanna Citti
Download or read book Geometric Methods in PDE’s written by Giovanna Citti and published by Springer. This book was released on 2015-10-31 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.
Book Synopsis Higher Complex Torsion and the Framing Principle by : Kiyoshi Igusa
Download or read book Higher Complex Torsion and the Framing Principle written by Kiyoshi Igusa and published by American Mathematical Soc.. This book was released on 2005 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intends to prove that higher Franz-Reidemeister (FR) torsion satisfies the transfer property and a formula known as the 'Framing Principle' in full generality. This title uses these properties to compute the higher FR-torsion for various smooth bundles with oriented closed even dimensional manifold fibers.
Book Synopsis Nonlinear Analysis on Manifolds. Monge-Ampère Equations by : Thierry Aubin
Download or read book Nonlinear Analysis on Manifolds. Monge-Ampère Equations written by Thierry Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
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:
Book Synopsis Differential Geometric Structures and Applications by : Vladimir Rovenski
Download or read book Differential Geometric Structures and Applications written by Vladimir Rovenski and published by Springer Nature. This book was released on with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lorentzian Geometry and Related Topics by : María A. Cañadas-Pinedo
Download or read book Lorentzian Geometry and Related Topics written by María A. Cañadas-Pinedo and published by Springer. This book was released on 2018-03-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of research papers and useful surveys by experts in the field which provide a representative picture of the current status of this fascinating area. Based on contributions from the VIII International Meeting on Lorentzian Geometry, held at the University of Málaga, Spain, this volume covers topics such as distinguished (maximal, trapped, null, spacelike, constant mean curvature, umbilical...) submanifolds, causal completion of spacetimes, stationary regions and horizons in spacetimes, solitons in semi-Riemannian manifolds, relation between Lorentzian and Finslerian geometries and the oscillator spacetime. In the last decades Lorentzian geometry has experienced a significant impulse, which has transformed it from just a mathematical tool for general relativity to a consolidated branch of differential geometry, interesting in and of itself. Nowadays, this field provides a framework where many different mathematical techniques arise with applications to multiple parts of mathematics and physics. This book is addressed to differential geometers, mathematical physicists and relativists, and graduate students interested in the field.
