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Symmetric hypersurfaces in Riemannian manifolds contracting to Lie-groups by their mean curvature

Calculus of Variations and Partial Differential Equations volume 4, pages 155–170 (1996)Cite this article

Abstract

This paper concerns the deformation by mean curvature of hypersurfaces M in Riemannian spaces Ñ that are invariant under a subgroup of the isometry-group on Ñ. We show that the hypersurfaces contract to this subgroup, if the cross-section satisfies a strong convexity assumption.

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Authors and Affiliations

  1. Department of Mathematics, Ruhr-University, Universitätsstrasse 150, D-44780, Bochum, Germany

    Knut Smoczyk

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  1. Knut Smoczyk
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Additional information

This forms part of the authors doctoral thesis and was carried out while the author was supported by a scholarship of the “Graduiertenkolleg für Geometrie und Mathematische Physik”.

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Smoczyk, K. Symmetric hypersurfaces in Riemannian manifolds contracting to Lie-groups by their mean curvature. Calc. Var 4, 155–170 (1996). https://doi.org/10.1007/BF01189952

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  • DOI: https://doi.org/10.1007/BF01189952

Mathematics subject classification (1991)

  • 53C45
  • 53C42
  • 35B40