Calculus of Variations and Partial Differential Equations

, Volume 39, Issue 3, pp 649–657

Moving surfaces by non-concave curvature functions

Article

DOI: 10.1007/s00526-010-0329-z

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 53C44Secondary 35K55

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.MSI, ANUCanberraAustralia