Moving surfaces by non-concave curvature functions
First Online: 29 April 2010 Received: 12 February 2010 Accepted: 28 March 2010 DOI:
Cite this article as: Andrews, B. Calc. Var. (2010) 39: 649. doi:10.1007/s00526-010-0329-z 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.
Mathematics Subject Classification (2000) Primary 53C44 Secondary 35K55
Communicated by L. Ambrosio.
Research supported by Discovery grants DP0344221 and DP0985802 of the Australian Research Council.
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