Geometric & Functional Analysis GAFA

, Volume 13, Issue 4, pp 915–933 | Cite as

Transience and capacity of minimal submanifolds

Original Article

Abstract

We prove explicit lower bounds for the capacity of annular domains of minimal submanifolds Pm in ambient Riemannian spaces Nn with sectional curvatures bounded from above. We characterize the situations in which the lower bounds for the capacity are actually attained. Furthermore we apply these bounds to prove that Brownian motion defined on a complete minimal submanifold is transient when the ambient space is a negatively curved Hadamard-Cartan manifold. The proof stems directly from the capacity bounds and also covers the case of minimal submanifolds of dimension m > 2 in Euclidean spaces.

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Mathematics Subject Classification (2000).

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Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Department of MathematicsTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Departament de Matemàtiques,Universitat Jaume ICastellonSpain

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