Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$
Abstract
Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flow at , generalizing a theorem for cylinders in [CM19b]. In the case of the -covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at .
Keywords
Cite
@article{arxiv.1909.02535,
title = {Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at $-\infty$},
author = {Douglas Stryker and Ao Sun},
journal= {arXiv preprint arXiv:1909.02535},
year = {2021}
}
Comments
17 pages. Modify the paper according to the referees' suggestion. In particular we remove Theorem 1.3 in the previous version, where there is a gap in the proof. Accepted by Communications in Contemporary Mathematics. arXiv admin note: text overlap with arXiv:1908.02688