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Loss of convexity and embeddedness for geometric evolution equations of higher order

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Abstract

We show that for a large class of geometric evolution equations of immersed surfaces in the Euclidean space, there are compact embedded surfaces that lose their embeddedness and compact strictly convex surfaces that lose their convexity under these evolution equations.

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  1. Albert-Einstein Institut, Am Mühlenberg 1, 14476, Postdam-Golm, Germany

    Simon Blatt

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  1. Simon Blatt
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Correspondence to Simon Blatt.

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Blatt, S. Loss of convexity and embeddedness for geometric evolution equations of higher order. J. Evol. Equ. 10, 21–27 (2010). https://doi.org/10.1007/s00028-009-0038-2

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  • DOI: https://doi.org/10.1007/s00028-009-0038-2

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