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