, Volume 38, Issue 4, pp 1365-1372
Date: 31 Oct 2012

Exit Times, Moment Problems and Comparison Theorems

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Abstract

We establish comparison theorems involving exit time moments for Brownian motion and eigenvalues for the Dirichlet problem for domains in a complete Riemannian manifold. These theorems are closely related to isoperimetric properties of the ambient manifold.