## p-Transience and p-Hyperbolicity of Submanifolds

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

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**p-Transience and p-Hyperbolicity of Submanifolds.** / Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente.

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

### Harvard

*p-Transience and p-Hyperbolicity of Submanifolds*. Department of Mathematics, Technical University of Denmark, Department of Mathematics, DTU. Mat-Report, no. 2006-18

### APA

*p-Transience and p-Hyperbolicity of Submanifolds*. Department of Mathematics, DTU: Department of Mathematics, Technical University of Denmark. (Mat-Report; No. 2006-18).

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### MLA

*p-Transience and p-Hyperbolicity of Submanifolds*Department of Mathematics, DTU: Department of Mathematics, Technical University of Denmark. 2006. (Mat-Report; Journal number 2006-18).

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### Bibtex

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### RIS

TY - RPRT

T1 - p-Transience and p-Hyperbolicity of Submanifolds

AU - Holopainen,Ilkka

AU - Markvorsen,Steen

AU - Palmer,Vicente

PY - 2006

Y1 - 2006

N2 - We use drifted Brownian motion in warped product model spaces as comparison constructions to show $p$-hyperbolicity of a large class of submanifolds for $p\ge 2$. The condition for $p$-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the submanifold. In the process of showing $p$-hyperbolicity we also obtain explicit lower bounds on the $p$-capacity of finite annular domains of the submanifolds in terms of the drifted $2$-capacity of the corresponding annuli in the respective comparison spaces.

AB - We use drifted Brownian motion in warped product model spaces as comparison constructions to show $p$-hyperbolicity of a large class of submanifolds for $p\ge 2$. The condition for $p$-hyperbolicity is expressed in terms of upper support functions for the radial sectional curvatures of the ambient space and for the radial convexity of the submanifold. In the process of showing $p$-hyperbolicity we also obtain explicit lower bounds on the $p$-capacity of finite annular domains of the submanifolds in terms of the drifted $2$-capacity of the corresponding annuli in the respective comparison spaces.

KW - p-Transience, p-hyperbolicity

KW - Submanifolds

KW - Comparison theory

M3 - Report

BT - p-Transience and p-Hyperbolicity of Submanifolds

PB - Department of Mathematics, Technical University of Denmark

ER -