Mean time exit and isoperimetric inequalities for minimal submanifolds of N

Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities, we establish a slightly better isoperimetric inequality and mean time exit estimates for minimal submanifolds of N × when N is non-positively curved. We prove isoperimetric inequalities for submanifolds with...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2009-04, Vol.41 (2), p.242-252
Main Authors: Bessa, G. Pacelli, Montenegro, J. Fabio
Format: Article
Language:English
Online Access:Get full text
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Summary:Based on Markvorsen and Palmer's work on mean time exit and isoperimetric inequalities, we establish a slightly better isoperimetric inequality and mean time exit estimates for minimal submanifolds of N × when N is non-positively curved. We prove isoperimetric inequalities for submanifolds with tamed second fundamental form in Hadamard spaces with bounded sectional curvature. We use mean time exit functions to show that spherically symmetric manifolds with geodesic spheres with exponential volume growth have a positive first eigenvalue.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdn121