Sharp pinching estimates for mean curvature flow in the sphere
Differential Geometry
2020-09-03 v1
Abstract
We prove a suite of asymptotically sharp quadratic curvature pinching estimates for mean curvature flow in the sphere which generalize Simons' rigidity theorem for minimal hypersurfaces. We then obtain derivative estimates for the second fundamental form which we utilize, via a compactness argument, to obtain a convexity estimate. Together, the convexity and cylindrical estimates yield a partial classification of singularity models. We also obtain new rigidity results for ancient solutions.
Cite
@article{arxiv.2009.00986,
title = {Sharp pinching estimates for mean curvature flow in the sphere},
author = {Mat Langford and Huy The Nguyen},
journal= {arXiv preprint arXiv:2009.00986},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:2006.08049