Potential Analysis

, Volume 36, Issue 1, pp 137–153 | Cite as

Comparison of Exit Moment Spectra for Extrinsic Metric Balls

Article

Abstract

We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as viewed from a pole in N. The bounds for the exit moment spectra are given in terms of the corresponding spectra for geodesic metric balls in suitably warped product model spaces. The bounds are sharp in the sense that equalities are obtained in characteristic cases. As a corollary we also obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds Nn themselves.

Keywords

Riemannian submanifolds Extrinsic balls Torsional rigidity L1-moment spectra Exit time Isoperimetric inequalities 

Mathematics Subject Classifications (2010)

Primary 53C42 58J65 35J25 60J65 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain
  2. 2.Department of MathematicsTechnical University of DenmarkLyngbyDenmark
  3. 3.Departament de Matemàtiques-Institute of New Imaging TechnologiesUniversitat Jaume ICastellónSpain

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