2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146300In 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.123 pages, 9 figures Ph.D. Dissertation Cornell University, 2006Metric Geometry58J35 (Primary) 60B15, 31C, 28A (Secondary)text