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Nonlinear degenerate curvature flows for weakly convex hypersurfaces

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Abstract.

We study the evolution of closed, weakly convex hypersurfaces in \(\mathbb{R}^{n + 1}\) in direction of their normal vector, where the speed equals a quotient of successive elementary symmetric polynomials of the principal curvatures. We show that there exists a solution for these weakly convex surfaces at least for some short time if the elementary symmetric polynomial in the denominator of the quotient is positive. The results for this nonlinear, degenerate flow are obtained by a cylindrically symmetric barrier construction.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Sabine Dieter

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  1. Sabine Dieter
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Correspondence to Sabine Dieter.

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Received: 10 November 2003, Accepted: 5 April 2004, Published online: 16 July 2004

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Dieter, S. Nonlinear degenerate curvature flows for weakly convex hypersurfaces. Cal Var 22, 229–251 (2005). https://doi.org/10.1007/s00526-004-0279-4

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  • DOI: https://doi.org/10.1007/s00526-004-0279-4

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