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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 using lower bounds on Ricci curvature.

Comparison Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds with a Lower Ricci Curvature Bound