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Volume Growth and Escape Rate of Brownian Motion on a Cartan—Hadamard Manifold

  • Alexander Grigor'yan
  • Elton Hsu
Part of the International Mathematical Series book series (IMAT, volume 9)

Abstract

We prove an upper bound for the escape rate of Brownian motion on a Cartan-Hadamard manifold in terms of the volume growth function. One of the ingredients of the proof is the Sobolev inequality on such manifolds.

Keywords

Rate Function Brownian Motion Riemannian Manifold Heat Equation Heat Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Alexander Grigor'yan
    • 1
  • Elton Hsu
    • 2
  1. 1.University of BielefeldGermany
  2. 2.Northwestern UniversityEvanstonUSA

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