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TORSIONAL RIGIDITY OF MINIMAL SUBMANIFOLDS

Published online by Cambridge University Press:  09 June 2006

STEEN MARKVORSEN  and
VICENTE PALMER
STEEN MARKVORSEN
Affiliation:
Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303 - DTU, DK–2800 Kgs. Lyngby, [email protected]
VICENTE PALMER
Affiliation:
Departament de Matemàtiques, Avd. Sos Baynat, s/n, Universitat Jaume I, 12071 Castellon, [email protected]
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Abstract

We prove explicit upper bounds for the torsional rigidity of extrinsic domains of minimal submanifolds $P^m$ in ambient Riemannian manifolds $N^n$ with a pole $p$. The upper bounds are given in terms of the torsional rigidities of corresponding Schwarz symmetrizations of the domains in warped product model spaces. Our main results are obtained via previously established isoperimetric inequalities, which are here extended to hold for this more general setting based on warped product comparison spaces. We also characterize the geometry of those situations in which the upper bounds for the torsional rigidity are actually attained and give conditions under which the geometric average of the stochastic mean exit time for Brownian motion at infinity is finite.

Keywords

53C4258J6535J2560J65
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 1 , July 2006 , pp. 253 - 272
Copyright
2006 London Mathematical Society

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