Ancient solutions of geometric flows with curvature pinching
Differential Geometry
2018-05-23 v3 Analysis of PDEs
Abstract
We prove rigidity theorems for ancient solutions of geometric flows of immersed submanifolds. Specifically, we find pinching conditions on the second fundamental form that characterize the shrinking sphere among compact ancient solutions for the mean curvature flow in codimension greater than one, and for some nonlinear curvature flows of hypersurfaces.
Keywords
Cite
@article{arxiv.1710.00361,
title = {Ancient solutions of geometric flows with curvature pinching},
author = {Susanna Risa and Carlo Sinestrari},
journal= {arXiv preprint arXiv:1710.00361},
year = {2018}
}
Comments
Minor changes, bibliography updated. To appear on The Journal of Geometric Analysis. The final version is available online at https://doi.org/10.1007/s12220-018-0036-0