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


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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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).

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Mathematics subject classification (1991)

  • 53C45
  • 53C42
  • 35B40