MPHA Seminar, Blocker 627, 16th November 2007, 1:50pm

Speaker: Melanie Pivarski, Texas A&M
Title: Small Time Heat Kernel Behavior on Riemannian Complexes

Abstract:
We will study how bounds on the local geometry of a Riemannian polyhedral
complex yield uniform local Poincare inequalities. These inequalities
have a variety of applications, including bounds on strong and weak
solutions to the heat equation, a local Harnack inequality, and stochastic
completeness.  We will additionally consider the example of a complex, X,
which has a finitely generated group of isomorphisms, G, such that X/G 
is a complex consisting of a finite number of polytopes.  When this
group, G, has polynomial volume growth, there is a uniform global
Poincare inequality on the complex, X.