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Torsional Rigidity of Minimal Submanifolds
Author(s) -
Markvorsen Steen,
Palmer Vicente
Publication year - 2006
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1017/s0024611505015716
Subject(s) - mathematics , isoperimetric inequality , rigidity (electromagnetism) , upper and lower bounds , infinity , brownian motion , pure mathematics , product (mathematics) , mathematical analysis , geometry , statistics , structural engineering , engineering
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. 2000 Mathematics Subject Classification 53C42, 58J65, 35J25, 60J65.