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Mean Curvature Flow with Triple Junctions in Higher Space Dimensions

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Abstract

We consider mean curvature flow of n-dimensional surface clusters. At (n−1)-dimensional triple junctions an angle condition is required which in the symmetric case reduces to the well-known 120° angle condition. Using a novel parametrization of evolving surface clusters and a new existence and regularity approach for parabolic equations on surface clusters we show local well-posedness by a contraction argument in parabolic Hölder spaces.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany

    Daniel Depner & Harald Garcke

  2. Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, 050-8585, Japan

    Yoshihito Kohsaka

Authors
  1. Daniel Depner
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  2. Harald Garcke
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  3. Yoshihito Kohsaka
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Corresponding author

Correspondence to Harald Garcke.

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Communicated by F. Otto

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Depner, D., Garcke, H. & Kohsaka, Y. Mean Curvature Flow with Triple Junctions in Higher Space Dimensions. Arch Rational Mech Anal 211, 301–334 (2014). https://doi.org/10.1007/s00205-013-0668-y

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  • DOI: https://doi.org/10.1007/s00205-013-0668-y

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