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

@article{Colladay2017ComparisonRE,
  title={Comparison Results, Exit Time Moments, and Eigenvalues on Riemannian Manifolds with a Lower Ricci Curvature Bound},
  author={D. Colladay and J. Langford and P. McDonald},
  journal={The Journal of Geometric Analysis},
  year={2017},
  volume={28},
  pages={3906-3927}
}
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.