JournalsrmiVol. 25, No. 2pp. 709–738

pp-Capacity and pp-Hyperbolicity of Submanifolds

  • Ilkka Holopainen

    University of Helsinki, Finland
  • Steen Markvorsen

    Technical University of Denmark, Lyngby, Denmark
  • Vicente Palmer

    Universitat Jaume I, Castellón, Spain
$p$-Capacity and $p$-Hyperbolicity of Submanifolds cover
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Abstract

We use explicit solutions to a drifted Laplace equation in warped product model spaces as comparison constructions to show pp-hyperbolicity of a large class of submanifolds for p2p\ge 2. The condition for pp-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 pp-hyperbolicity we also obtain explicit lower bounds on the pp-capacity of finite annular domains of the submanifolds in terms of the drifted 22-capacity of the corresponding annuli in the respective comparison spaces.

Cite this article

Ilkka Holopainen, Steen Markvorsen, Vicente Palmer, pp-Capacity and pp-Hyperbolicity of Submanifolds. Rev. Mat. Iberoam. 25 (2009), no. 2, pp. 709–738

DOI 10.4171/RMI/580