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Mean curvature flow through singularities for surfaces of rotation

1995; Springer Science+Business Media; Volume: 5; Issue: 3 Linguagem: Inglês

10.1007/bf02921800

1559-002X

Steven J. Altschuler, Sigurd Angenent, Yoshikazu Giga,

Navier-Stokes equation solutions

In this paper, we study generalized "viscosity" solutions of the mean curvature evolution which were introduced by Chen, Giga, and Goto and by Evans and Spruck. We devote much of our attention to solutions whose initial value is a compact, smooth, rotationally symmetric hypersurface given by rotating a graph around an axis. Our main result is the regularity of the solution except at isolated points in spacetime and estimates on the number of such points.