Abstract
A convex surface contracting by a strictly monotone, homogeneous degree one function of its principal curvatures remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the concavity of the speed as a function of principal curvatures. We also discuss motion by functions homogeneous of degree greater than 1 in the principal curvatures.
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Communicated by L. Ambrosio.
Research supported by Discovery grants DP0344221 and DP0985802 of the Australian Research Council.
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Andrews, B. Moving surfaces by non-concave curvature functions. Calc. Var. 39, 649–657 (2010). https://doi.org/10.1007/s00526-010-0329-z
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DOI: https://doi.org/10.1007/s00526-010-0329-z