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Multiplicative Functional for the Heat Equation on Manifolds with Boundary

  • Cheng Ouyang
Conference paper
Part of the Progress in Probability book series (PRPR, volume 72)

Abstract

The multiplicative functional for the heat equation on k-forms with absolute boundary condition is constructed and a probabilistic representation of the solution is obtained. As an application, we prove a heat kernel domination that was previously discussed by Donnelly and Li, and Shigekawa.

Keywords

Absolute boundary condition Gradient inequality Heat kernel domination Hodge-de Rham Laplacian Riemannian manifold with boundary 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA

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