Torsional Rigidity of Minimal Submanifolds

Publication: Research - peer-reviewJournal article – Annual report year: 2006

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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.
Original languageEnglish
JournalProceedings of the London Mathematical Society
Publication date2006
Volume93
Issue3
Pages253-272
ISSN0024-6115
DOIs
StatePublished
CitationsWeb of Science® Times Cited: No match on DOI

Keywords

  • Isoperimetric inequalities, Torsional rigidity, Minimal submanifolds
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