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arXiv · 1207.2351

Mean curvature flow with triple junctions in higher space dimensions

Daniel Depner·Harald Garcke·Yoshihito Kohsaka
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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 degree 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 Hoelder spaces.

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Daniel Depner, Harald Garcke, Yoshihito Kohsaka. 2012-07-10. Mean curvature flow with triple junctions in higher space dimensions. https://doi.org/10.1007/s00205-013-0668-y

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