(1) Department of Mathematics, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark;(2) Departament de Matemàtiques,, Universitat Jaume I, 12071 Castellon, Spain
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.