Interior estimates and longtime solutions for mean curvature flow of noncompact spacelike hypersurfaces in Minkowski space
For entire graphs defining spacelike hypersurfaces in Minkowski space which are moving by mean curvature, the author proves the following Theorem: For any smooth initial data \(u_0:{\mathbb R}^n\to{\mathbb R}\) defining a spacelike hypersurface the mean curvature flow has a smooth spacelike solution for all \(t>0\). The proof is done by solving corresponding boundary value problems on increasing domains of radius \(k\) and selecting a converging subsequence of solutions for \(k\to\infty\). The longtime existence of solutions for these boundary value problems is shown in the first part of the paper by deriving appropriate interior estimates.
scientific article; zbMATH DE number 1145658
scientific article