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Partial regularity of weak solutions for the curve shortening flow

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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 ½.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universtiy of Sussex, Falmer, Brighton BN1 9QH, UK. e-mail: k.p.deckelnick@sussex.ac.uk, , , , , , UK

    Klaus Deckelnick

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  1. Klaus Deckelnick
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Received: 23 May 1998 / Revised version: 7 September 1998

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Deckelnick, K. Partial regularity of weak solutions for the curve shortening flow. manuscripta math. 98, 265–274 (1999). https://doi.org/10.1007/s002290050139

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  • DOI: https://doi.org/10.1007/s002290050139

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