Heat kernels on Euclidean complexes

Details Heat kernels on Euclidean complexes Heat kernels on Euclidean complexes

2008-01-21

arxiv.org/abs/0801.3038v1

Mathematics

Metric Geometry

123 pages, 9 figures Ph.D. Dissertation Cornell University, 2006

Scientific paper

In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincare inequality for complexes with bounded geometry and use this to determine uniform small time heat kernel bounds via a theorem of Sturm. We then consider such complexes with an underlying finitely generated group structure. We use techniques of Saloff-Coste and Pittet to show a large time asymptotic equivalence for the heat kernel on the complex and the heat kernel on the group.

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