Analysis on Riemannian co-compact covers

L. Saloff‐Coste

Type: Article

Publication Date: 2004-01-01

Citations: 29

DOI: https://doi.org/10.4310/sdg.2004.v9.n1.a10

Abstract

This is a survey on analysis on non-compact co-compact Riemannian covers and how it relates to random walks on finitely generated groups.The focus is on the long time behavior of the heat kernel and related topics such as Liouville theorems, scale invariant Harnack inequalities and isoperimetric profiles. Contents1. Introduction 351 2. Some quasi-isometric invariants 356 3. Invariance of the heat decay 366 4. The heat decay for random walks 367 5. Harmonic functions 373

Locations

Surveys in Differential Geometry - View - PDF

Similar Works

Action	Title	Year	Authors
+	On the strong liouville property for co-compact Riemannian covers	1994	Martine Babillot Philippe Bougerol Laure Élie
+	A survey of Ricci curvature for metric spaces and Markov chains	2019	Yann Ollivier
+	Riemannian Coverings	2006	Isaac Chavel
+	Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups	2011	Fabrice Baudoin Maria Gordina Tai Melcher
+	Ergodic theory on compact metric spaces	2010	Feliks Przytycki Mariusz Urbański
+	Heat kernel estimates and Riesz transforms on some Riemannian covering manifolds	2004	Nick Dungey
+ PDF Chat	Heat content asymptotics for sub-Riemannian manifolds	2020	Luca Rizzi Tommaso Rossi
+	Metric measure spaces with Ricci bounds from below	2024	Shouhei Honda
+ PDF Chat	Quasi-invariance for heat kernel measures on sub-Riemannian infinite-dimensional Heisenberg groups	2012	Fabrice Baudoin Maria Gordina Tai Melcher
+	Random Walks and Heat Kernels on Graphs	2017	Martin T. Barlow
+	Ergodic Theory and Geometric Measures	2023	Janina Kotus Mariusz Urbański
+ PDF Chat	Heat kernels on covering spaces and topological invariants	1993	John Lott
+	The heat flow on metric random walk spaces	2019	José M. Mazón Marcos Solera J. Toledo
+	Heat kernel estimates, Sobolev-type inequalities and Riesz transform on noncompact Riemannian manifolds	2013	Thierry Coulhon
+	Heat kernels and analysis on manifolds, graphs, and metric spaces : lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France	2003	Pascal Auscher Thierry Coulhon Alexander Grigor’yan
+	From Harnack inequality to heat kernel estimates on metric measure spaces and applications	2019	Luca Tamanini
+ PDF Chat	Linear Drift and Entropy for Regular Covers	2010	François Ledrappier
+	Harnack inequalities and Gaussian estimates for random walks on metric measure spaces	2015	Mathav Murugan Laurent Saloff‐Coste
+ PDF Chat	Harnack inequalities and Gaussian estimates for random walks on metric measure spaces	2023	Mathav Murugan Laurent Saloff‐Coste
+	Ergodic properties of smooth hyperbolic measures	2013	Luís Barreira Yakov Pesin

Works That Cite This (28)

Action	Title	Year	Authors
+ PDF Chat	Large-scale Sobolev inequalities on metric measure spaces and applications	2008	Romain Tessera
+ PDF Chat	Stability of the elliptic Harnack inequality	2018	Martin T. Barlow Mathav Murugan
+	Asymptotic isoperimetry of balls in metric measure spaces	2005	Romain Tessera
+ PDF Chat	Isoperimetry of group actions	2008	Piotr W. Nowak
+ PDF Chat	Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks	2006	Anna Erschler
+ PDF Chat	Green's function asymptotics of periodic elliptic operators on abelian coverings of compact manifolds	2017	Minh Kha
+	Liouville-Riemann-Roch Theorems on Abelian Coverings	2021	Minh Kha Peter Kuchment
+	Perspectives on geometric analysis	2006	Shing‐Tung Yau
+	Large scale Sobolev inequalities on metric measure spaces and applications	2007	Romain Tessera
+	Functions with finite Dirichlet sum of order $p$ and quasi-monomorphisms of infinite graphs	2012	Tae Hattori Atsushi Kasue

Works Cited by This (93)

Action	Title	Year	Authors
+ PDF Chat	Instability of the Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains	1987	Terry Lyons
+	Poisson Boundaries of Random Walks on Discrete Solvable Groups	1991	Vadim A. Kaimanovich
+	Metric Structures for Riemannian and Non-Riemannian Spaces	2007	Mikhael Gromov
+	Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives	2001	Isaac Chavel
+	Three-Dimensional Geometry and Topology	1997	William P. Thurston Silvio Levy
+	Discrete Subgroups of Lie Groups	1972	M. S. Raghunathan
+	None	2003	Anna Erschler
+ PDF Chat	Random walks on abelian-by-cyclic groups	2002	Christophe Pittet Laurent Saloff‐Coste
+	Convex functions and Orlicz spaces	1961	M. A. Krasnosel’skii I︠a︡. B. Rutit︠s︡kiĭ Leo F. Boron
+ PDF Chat	Growth of finitely generated solvable groups	1968	John Milnor