Heat Kernel and Analysis on Manifolds

Heat Kernel and Analysis on Manifolds
Title Heat Kernel and Analysis on Manifolds PDF eBook
Author Alexander Grigoryan
Publisher American Mathematical Soc.
Pages 504
Release 2009
Genre Education
ISBN 0821893939

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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.

Heat Kernel and Analysis on Manifolds

Heat Kernel and Analysis on Manifolds
Title Heat Kernel and Analysis on Manifolds PDF eBook
Author Alexander Grigoryan
Publisher American Mathematical Soc.
Pages 504
Release 2009
Genre Mathematics
ISBN 0821849352

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"This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and p -Laplace operators, heat kernel and spherical inversion on SL 2 (C) , random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs."--Publisher's website.

The Laplacian on a Riemannian Manifold

The Laplacian on a Riemannian Manifold
Title The Laplacian on a Riemannian Manifold PDF eBook
Author Steven Rosenberg
Publisher Cambridge University Press
Pages 190
Release 1997-01-09
Genre Mathematics
ISBN 9780521468312

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This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Heat Kernels and Spectral Theory

Heat Kernels and Spectral Theory
Title Heat Kernels and Spectral Theory PDF eBook
Author E. B. Davies
Publisher Cambridge University Press
Pages 212
Release 1989
Genre Mathematics
ISBN 9780521409971

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Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators.

Heat Kernels and Dirac Operators

Heat Kernels and Dirac Operators
Title Heat Kernels and Dirac Operators PDF eBook
Author Nicole Berline
Publisher Springer Science & Business Media
Pages 384
Release 2003-12-08
Genre Mathematics
ISBN 9783540200628

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In the first edition of this book, simple proofs of the Atiyah-Singer Index Theorem for Dirac operators on compact Riemannian manifolds and its generalizations (due to the authors and J.-M. Bismut) were presented, using an explicit geometric construction of the heat kernel of a generalized Dirac operator; the new edition makes this popular book available to students and researchers in an attractive paperback.

Analysis and Geometry on Graphs and Manifolds

Analysis and Geometry on Graphs and Manifolds
Title Analysis and Geometry on Graphs and Manifolds PDF eBook
Author Matthias Keller
Publisher Cambridge University Press
Pages 493
Release 2020-08-20
Genre Mathematics
ISBN 1108587380

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This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.

Stochastic Analysis on Manifolds

Stochastic Analysis on Manifolds
Title Stochastic Analysis on Manifolds PDF eBook
Author Elton P. Hsu
Publisher American Mathematical Soc.
Pages 297
Release 2002
Genre Mathematics
ISBN 0821808028

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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.