Moving surfaces by non-concave curvature functions. (English) Zbl 1203.53062

Andrews, Ben

Calc. Var. Partial Differ. Equ. 39, No. 3-4, 649-657 (2010).

Summary: 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.

MSC:

53C44	Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35K55	Nonlinear parabolic equations

Keywords:

convex surface; function of principal curvatures

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