## Torsional Rigidity of Minimal Submanifolds

Publication: Research - peer-review › Journal article – Annual report year: 2006

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**Torsional Rigidity of Minimal Submanifolds.** / Markvorsen, Steen; Palmer, Vicente.

Publication: Research - peer-review › Journal article – Annual report year: 2006

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*Proceedings of the London Mathematical Society*, vol 93, no. 3, pp. 253-272., 10.1112/S0024611505015716

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*Proceedings of the London Mathematical Society*,

*93*(3), 253-272. 10.1112/S0024611505015716

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*Proceedings of the London Mathematical Society*. 2006, 93(3). 253-272. Available: 10.1112/S0024611505015716

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### RIS

TY - JOUR

T1 - Torsional Rigidity of Minimal Submanifolds

AU - Markvorsen,Steen

AU - Palmer,Vicente

PB - Oxford University Press

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Isoperimetric inequalities

KW - Torsional rigidity

KW - Minimal submanifolds

U2 - 10.1112/S0024611505015716

DO - 10.1112/S0024611505015716

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 3

VL - 93

SP - 253

EP - 272

ER -