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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces

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Brand new. We distribute directly for the publisher. This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincar 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.This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds. Read more Show Less

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Overview

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris) on heat kernels, random walks, and analysis on manifolds and graphs. 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. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

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Product Details

Table of Contents

Preface
Some questions on elliptic operators 1
Heat kernels and sets with fractal structure 11
Brownian motions on compact groups of infinite dimension 41
Heat kernel and isoperimetry on non-compact Riemanuian manifolds 65
Heat kernels measures and infinite dimensional analysis 101
Heat kernels and functional theory on metric measure spaces 143
Sobolev spaces on metric-measure spaces 173
Quasiregular mappings and the p-Laplace operator 219
Spherical inversion on SL[subscript 2](C) 241
Spectral geometry of crystal lattices 271
Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces 307
Some topics related to analysis on metric spaces 341
Probability measures on metric spaces of nonpositive curvature 357
Generating function techniques for random walks on graphs 391
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