Surveys in Differential Geometry
Volume 9 (2004)
Analysis on Riemannian co-compact covers
Pages: 351 – 384
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.