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

title={Comparison Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds with a Lower Ricci Curvature Bound},
author={Don Colladay and Jeffrey J. Langford and Patrick McDonald},
journal={The Journal of Geometric Analysis},
year={2017},
volume={28},
pages={3906-3927}
}
• Published 6 June 2017
• Mathematics
• The Journal of Geometric Analysis
We study the relationship between the geometry of smoothly bounded domains in complete Riemannian manifolds and the associated sequence of $$L^1$$L1-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.
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