Nonlinear degenerate curvature flows for weakly convex hypersurfaces

Dieter, Sabine
February 2005
Calculus of Variations & Partial Differential Equations;Feb2005, Vol. 22 Issue 2, p229
Academic Journal
We study the evolution of closed, weakly convex hypersurfaces inin direction of their normal vector, where the speed equals a quotient of successive elementary symmetric polynomials of the principal curvatures. We show that there exists a solution for these weakly convex surfaces at least for some short time if the elementary symmetric polynomial in the denominator of the quotient is positive. The results for this nonlinear, degenerate flow are obtained by a cylindrically symmetric barrier construction.


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