Comparison Results, Exit Time Moments, And Eigenvalues On Riemannian Manifolds With A Lower Ricci Curvature Bound

We study the relationship between the geometry of smoothly bounded domains in complete Riemannian manifolds and the associated sequence of $L^1$-norms of exit time moments for Brownian motion. We establish bounds for Dirichlet eigenvalues and, for closed manifolds, we establish a comparison result for elements of the moment sequence.