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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
Edited by: Pascal Auscher, Université Paris-Sud, Orsay, France, Thierry Coulhon, Université de Cergy-Pontoise, Cergy Pontoise, France, and Alexander Grigor'yan, Imperial College London, UK

Contemporary Mathematics
2003; 424 pp; softcover
Volume: 338
ISBN-10: 0-8218-3383-9
ISBN-13: 978-0-8218-3383-4
List Price: US$109
Member Price: US$87.20
Order Code: CONM/338
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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.

This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.


Graduate students and research mathematicians interested in random processes and analysis on manifolds.

Table of Contents

  • P. Auscher -- Some questions on elliptic operators
  • M. T. Barlow -- Heat kernels and sets with fractal structure
  • A. Bendikov and L. Saloff-Coste -- Brownian motions on compact groups of infinite dimension
  • T. Coulhon -- Heat kernel and isoperimetry on non-compact Riemannian manifolds
  • B. K. Driver -- Heat kernels measures and infinite dimensional analysis
  • A. Grigor'yan -- Heat kernels and function theory on metric measure spaces
  • P. Hajłasz -- Sobolev spaces on metric-measure spaces
  • I. Holopainen -- Quasiregular mappings and the \(p\)-Laplace operator
  • J. Jorgenson and S. Lang -- Spherical inversion on SL\(_2\)(C)
  • M. Kotani and T. Sunada -- Spectral geometry of crystal lattices
  • V. Maz'ya -- Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces
  • S. Semmes -- Some topics related to analysis on metric spaces
  • K.-T. Sturm -- Probability measures on metric spaces of nonpositive curvature
  • W. Woess -- Generating function techniques for random walks on graphs
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