Strong spherical rigidity of ancient solutions of expansive curvature flows
arXiv:1907.12319 · doi:10.1112/blms.12308
Abstract
We consider geometric flows of hypersurfaces expanding by a function of the extrinsic curvature and we show that the homothethic sphere is the unique solution of the flow which converges to a point at the initial time. The result does not require assumptions on the speed other than positivity and monotonicity and it is proved using a reflection argument. Our theorem shows that expanding flows exhibit stronger spherical rigidity, if compared with the classification results of ancient solutions in the contractive case.
Minor corrections. 9 pages. Published on Bulletin of the London Mathematical Society, Vol. 52 (1), 94-99