-Capacity and -Hyperbolicity of Submanifolds

  • Ilkka Holopainen

    University of Helsinki, Finland
  • Steen Markvorsen

    Technical University of Denmark, Lyngby, Denmark
  • Vicente Palmer

    Universitat Jaume I, Castellón, Spain


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

Cite this article

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

DOI 10.4171/RMI/580