Geometry And Analysis On Manifolds
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Geometry And Analysis On Manifolds
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Author : Takushiro Ochiai
language : en
Publisher: Springer
Release Date : 2015-02-25
Geometry And Analysis On Manifolds written by Takushiro Ochiai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.
Stochastic Analysis On Manifolds
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Author : Elton P. Hsu
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Stochastic Analysis On Manifolds written by Elton P. Hsu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Mainly from the perspective of a probabilist, Hsu shows how stochastic analysis and differential geometry can work together for their mutual benefit. He writes for researchers and advanced graduate students with a firm foundation in basic euclidean stochastic analysis, and differential geometry. He does not include the exercises usual to such texts, but does provide proofs throughout that invite readers to test their understanding. Annotation copyrighted by Book News Inc., Portland, OR.
Differential Geometry And Analysis On Cr Manifolds
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Author : Sorin Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-10
Differential Geometry And Analysis On Cr Manifolds written by Sorin Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-10 with Mathematics categories.
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study
Analysis Manifolds And Physics Revised Edition
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Author : Yvonne Choquet-Bruhat
language : en
Publisher: Gulf Professional Publishing
Release Date : 1982
Analysis Manifolds And Physics Revised Edition written by Yvonne Choquet-Bruhat and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Tensor Analysis On Manifolds
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Author : Richard L. Bishop
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Tensor Analysis On Manifolds written by Richard L. Bishop and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds
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Author : Bruno Bianchini
language : en
Publisher: Springer Nature
Release Date : 2021-01-18
Geometric Analysis Of Quasilinear Inequalities On Complete Manifolds written by Bruno Bianchini and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Mathematics categories.
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Heat Kernel And Analysis On Manifolds
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Author : Alexander Grigoryan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Heat Kernel And Analysis On Manifolds written by Alexander Grigoryan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Education categories.
The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.
Nonlinear Analysis On Manifolds Monge Amp Re Equations
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Author : Thierry Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Analysis On Manifolds Monge Amp Re Equations written by Thierry Aubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Differential Analysis On Complex Manifolds
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Author : Raymond O. Wells
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-31
Differential Analysis On Complex Manifolds written by Raymond O. Wells and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-31 with Mathematics categories.
A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
An Introduction To The Analysis Of Paths On A Riemannian Manifold
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Author : Daniel W. Stroock
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
An Introduction To The Analysis Of Paths On A Riemannian Manifold written by Daniel W. Stroock and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Hoping to make the text more accessible to readers not schooled in the probabalistic tradition, Stroock (affiliation unspecified) emphasizes the geometric over the stochastic analysis of differential manifolds. Chapters deconstruct Brownian paths, diffusions in Euclidean space, intrinsic and extrinsic Riemannian geometry, Bocher's identity, and the bundle of orthonormal frames. The volume humbly concludes with an "admission of defeat" in regard to recovering the Li-Yau basic differential inequality. Annotation copyrighted by Book News, Inc., Portland, OR.