The Journal of Geometric Analysis

, Volume 28, Issue 4, pp 3906–3927 | Cite as

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

  • Don Colladay
  • Jeffrey J. LangfordEmail author
  • Patrick McDonald


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.


Torsional rigidity Heat content Dirichlet Problem Brownian motion 

Mathematics Subject Classification

58J65 58J50 35P15 


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Copyright information

© Mathematica Josephina, Inc. 2018

Authors and Affiliations

  • Don Colladay
    • 2
  • Jeffrey J. Langford
    • 1
    Email author
  • Patrick McDonald
    • 2
  1. 1.Department of MathematicsBucknell UniversityLewisburgUSA
  2. 2.Division of Natural ScienceNew College of FloridaSarasotaUSA

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