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Bulletin of the London Mathematical Society Advance Access originally published online on February 8, 2009
Bulletin of the London Mathematical Society 2009 41(2):242-252; doi:10.1112/blms/bdn121
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© 2009 London Mathematical Society

Mean time exit and isoperimetric inequalities for minimal submanifolds of NxR

G. Pacelli Bessa and J. Fabio Montenegro

Departamento de Matematica
Universidade Federal do Ceara
Bloco 914, 60455-760 Fortaleza, Ceara
Brazil
fabio@mat.ufc.br

Received 24 April 2008. Revision received 19 September 2008.

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 x R 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.

Às minhas três Marias

2000 Mathematics Subject Classification 53C42 (primary), 58J65 (secondary).

The authors were partially supported by CNPq-FUNCAP.


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