Strong spherical rigidity of ancient solutions of expansive curvature flows
Differential Geometry
2020-05-05 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1907.12319,
title = {Strong spherical rigidity of ancient solutions of expansive curvature flows},
author = {Susanna Risa and Carlo Sinestrari},
journal= {arXiv preprint arXiv:1907.12319},
year = {2020}
}
Comments
Minor corrections. 9 pages. Published on Bulletin of the London Mathematical Society, Vol. 52 (1), 94-99