Rigidity and {\L}ojasiewicz inequalities for Clifford self-shrinkers
Differential Geometry
2020-11-04 v1
Abstract
We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit {\L}ojasiewicz inequalities near such products. {\L}ojasiewicz inequalities were previously used by Schulze to prove uniqueness of tangent mean curvature flows at compact shrinkers; our results provide an explicit rate of convergence to products of two spheres.
Cite
@article{arxiv.2011.01636,
title = {Rigidity and {\L}ojasiewicz inequalities for Clifford self-shrinkers},
author = {Ao Sun and Jonathan J. Zhu},
journal= {arXiv preprint arXiv:2011.01636},
year = {2020}
}
Comments
31 pages, comments welcome!