Partial regularity of weak solutions for the curve shortening flow |
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Authors: | Klaus Deckelnick |
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Institution: | (1) School of Mathematical Sciences, Universtiy of Sussex, Falmer, Brighton BN1 9QH, UK. e-mail: k.p.deckelnick@sussex.ac.uk, UK |
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Abstract: | We study the regularity of certain weak solutions for the curve shortening flow in arbitrary codimension. These solutions
arise as limits of a regularization process which is related to an approach suggested by Calabi. We prove that the set of
times for which such a weak solution is not smooth has Hausdorff dimension at most ?.
Received: 23 May 1998 / Revised version: 7 September 1998 |
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Keywords: | Mathematics Subject Classification (1991):35K45 35K65 |
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