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Melanie Pivarski and Laurent Saloff-Coste
Small time heat kernel behavior on Riemannian complexes
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| Published: |
September 30, 2008 |
| Keywords: |
Poincaré inequality, heat kernel, heat equation, polynomial growth group, Euclidean complex, Riemannian complex, polytopal complex, polyhedral complex |
| Subject: |
26D10, 35B40, 43A85, 57S, 58J35 |
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Abstract
We study how bounds on the local geometry of a
Riemannian polyhedral complex yield uniform local Poincaré
inequalities. These inequalities have a variety of applications,
including bounds on the heat kernel and a uniform local Harnack
inequality. We additionally consider the example of a complex, X,
which has a finitely generated group of isomorphisms, G, such that
X/G =Y is a complex consisting of a finite number of polytopes.
We show that when this group, G, has polynomial volume growth,
there is a uniform global Poincaré inequality on the complex,
X.
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| Acknowledgements
Pivarski's research was partially supported by NSF Grant DMS 0306194; Saloff-Coste's research was partially supported by NSF Grant DMS 0603886.
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| Author information
Melanie Pivarski:
Texas A&M University, College Station, TX 77843 USA
pivarski@math.tamu.edu
Laurent Saloff-Coste:
Cornell University, Ithaca, NY 15843 USA
lsc@math.cornell.edu
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