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June, 2009 $p$-Capacity and $p$-Hyperbolicity of Submanifolds
Ilkka Holopainen , Steen Markvorsen , Vicente Palmer
Rev. Mat. Iberoamericana 25(2): 709-738 (June, 2009).


We use explicit solutions to a drifted Laplace equation 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.


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Ilkka Holopainen . Steen Markvorsen . Vicente Palmer . "$p$-Capacity and $p$-Hyperbolicity of Submanifolds." Rev. Mat. Iberoamericana 25 (2) 709 - 738, June, 2009.


Published: June, 2009
First available in Project Euclid: 13 October 2009

zbMATH: 1176.53056
MathSciNet: MR2569551

Primary: 31C12 , 53C40
Secondary: 31C45 , 53C21 , 60J65

Keywords: $p$-Laplacian , capacity , comparison theory , Hyperbolicity , Isoperimetric inequality , parabolicity , Submanifolds , transience

Rights: Copyright © 2009 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.25 • No. 2 • June, 2009
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