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On Deciding Whether a Submanifold Is Parabolic or Hyperbolic Using Its Mean Curvature

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Topics in Modern Differential Geometry

Part of the book series: Atlantis Transactions in Geometry ((ATLANTIS,volume 1))

Abstract

We are going to see how the Hessian-Index analysis of the extrinsic distance function defined on a submanifold give us a geometric description of some of its functional theoretic properties such as its parabolicity/hyperbolicity.

Work partially supported by the Caixa Castelló Foundation and DGI grant MTM2007-62344.

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Authors and Affiliations

  1. Departament de Matemàtiques-Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Castellon, Spain

    Vicente Palmer

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  1. Vicente Palmer
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Correspondence to Vicente Palmer .

Editor information

Editors and Affiliations

  1. Department of Teacher Education, Thomas More University College Department of Teacher Education, Vorselaar, Belgium

    Stefan Haesen

  2. Department of Mathematics, University of Leuven Department of Mathematics, Leuven, Belgium

    Leopold Verstraelen

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Palmer, V. (2017). On Deciding Whether a Submanifold Is Parabolic or Hyperbolic Using Its Mean Curvature. In: Haesen, S., Verstraelen, L. (eds) Topics in Modern Differential Geometry. Atlantis Transactions in Geometry, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-240-3_4

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