Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
About this Title
Pascal Auscher, Thierry Coulhon and Alexander Grigor’yan, Editors
Publication: Contemporary Mathematics
Publication Year : Volume 338
ISBNs: 978-0-8218-3383-4 (print); 978-0-8218-7928-3 (online)
MathSciNet review: 2041910
This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré 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.
Graduate students and research mathematicians interested in random processes and analysis on manifolds.
Table of Contents
- Pascal Auscher – Some questions on elliptic operators [MR 2039949]
- Martin T. Barlow – Heat kernels and sets with fractal structure [MR 2039950]
- Alexander Bendikov and Laurent Saloff-Coste – Brownian motions on compact groups of infinite dimension [MR 2039951]
- Thierry Coulhon – Heat kernel and isoperimetry on non-compact Riemannian manifolds [MR 2039952]
- Bruce K. Driver – Heat kernels measures and infinite dimensional analysis [MR 2039953]
- Alexander Grigor’yan – Heat kernels and function theory on metric measure spaces [MR 2039954]
- Piotr Hajłasz – Sobolev spaces on metric-measure spaces [MR 2039955]
- Ilkka Holopainen – Quasiregular mappings and the -Laplace operator [MR 2039956]
- Jay Jorgenson and Serge Lang – Spherical inversion on [MR 2039957]
- Motoko Kotani and Toshikazu Sunada – Spectral geometry of crystal lattices [MR 2039958]
- Vladimir Maz′ya – Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces [MR 2039959]
- Stephen Semmes – Some topics related to analysis on metric spaces
- Karl-Theodor Sturm – Probability measures on metric spaces of nonpositive curvature [MR 2039961]
- Wolfgang Woess – Generating function techniques for random walks on graphs [MR 2039962]