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

Don Colladay; Jeffrey J. Langford; Patrick McDonald

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

Spectral Theory 2017-06-14 v2

Authors: Don Colladay , Jeffrey J. Langford , Patrick McDonald

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.

Keywords

Riemannian manifolds Ricci curvature bound exit time moments Dirichlet eigenvalues Brownian motion comparison result

Cite

@article{arxiv.1706.01601,
  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= {arXiv preprint arXiv:1706.01601},
  year   = {2017}
}

Comments

21 pages. Added results for the case of equality

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

Abstract

Keywords

Cite

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