## Revista Matemática Iberoamericana

### $p$-Capacity and $p$-Hyperbolicity of Submanifolds

#### Abstract

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.

#### Article information

Source
Rev. Mat. Iberoamericana, Volume 25, Number 2 (2009), 709-738.

Dates
First available in Project Euclid: 13 October 2009

https://projecteuclid.org/euclid.rmi/1255440072

Mathematical Reviews number (MathSciNet)
MR2569551

Zentralblatt MATH identifier
1176.53056

#### Citation

Holopainen, Ilkka; Markvorsen, Steen; Palmer, Vicente. $p$-Capacity and $p$-Hyperbolicity of Submanifolds. Rev. Mat. Iberoamericana 25 (2009), no. 2, 709--738. https://projecteuclid.org/euclid.rmi/1255440072

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