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

Don Colladay; Jeffrey J. Langford; Patrick McDonald

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arXiv · 1706.01601

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

Don Colladay·Jeffrey J. Langford·Patrick McDonald

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Abstract

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.

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BibTeX RIS

Don Colladay, Jeffrey J. Langford, Patrick McDonald. 2017-06-06. Comparison Results, Exit Time Moments, And Eigenvalues On Riemannian Manifolds With A Lower Ricci Curvature Bound. https://arxiv.org/abs/1706.01601

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