p-Transience and p-Hyperbolicity of Submanifolds

Publication: Research - peer-reviewReport – Annual report year: 2006

Standard

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

Department of Mathematics, DTU : Department of Mathematics, Technical University of Denmark, 2006. 17 p. (Mat-Report; No. 2006-18).

Publication: Research - peer-reviewReport – Annual report year: 2006

Harvard

Holopainen, I, Markvorsen, S & Palmer, V 2006, p-Transience and p-Hyperbolicity of Submanifolds. Department of Mathematics, Technical University of Denmark, Department of Mathematics, DTU. Mat-Report, no. 2006-18

APA

Holopainen, I., Markvorsen, S., & Palmer, V. (2006). p-Transience and p-Hyperbolicity of Submanifolds. Department of Mathematics, DTU: Department of Mathematics, Technical University of Denmark. (Mat-Report; No. 2006-18).

CBE

Holopainen I, Markvorsen S, Palmer V 2006. p-Transience and p-Hyperbolicity of Submanifolds. Department of Mathematics, DTU: Department of Mathematics, Technical University of Denmark. 17 p. (Mat-Report; No. 2006-18).

MLA

Holopainen, Ilkka, Steen Markvorsen and Vicente Palmer 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).

Vancouver

Holopainen I, Markvorsen S, Palmer V. p-Transience and p-Hyperbolicity of Submanifolds. Department of Mathematics, DTU: Department of Mathematics, Technical University of Denmark, 2006. 17 p. (Mat-Report; No. 2006-18).

Author

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

Department of Mathematics, DTU : Department of Mathematics, Technical University of Denmark, 2006. 17 p. (Mat-Report; No. 2006-18).

Publication: Research - peer-reviewReport – Annual report year: 2006

Bibtex

@book{2b93114b673d4bedbefd438c0ae42ba4,
title = "p-Transience and p-Hyperbolicity of Submanifolds",
keywords = "p-Transience, p-hyperbolicity, Submanifolds, Comparison theory",
publisher = "Department of Mathematics, Technical University of Denmark",
author = "Ilkka Holopainen and Steen Markvorsen and Vicente Palmer",
year = "2006",
series = "Mat-Report",

}

RIS

TY - RPRT

T1 - p-Transience and p-Hyperbolicity of Submanifolds

A1 - Holopainen,Ilkka

A1 - Markvorsen,Steen

A1 - Palmer,Vicente

AU - Holopainen,Ilkka

AU - Markvorsen,Steen

AU - Palmer,Vicente

PB - Department of Mathematics, Technical University of Denmark

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

BT - p-Transience and p-Hyperbolicity of Submanifolds

T3 - Mat-Report

T3 - en_GB

ER -