A maximum principle for self-shrinkers and some consequences
Differential Geometry
2014-12-16 v1
Abstract
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result about the asymptotic behavior of self-shrinkers. This comparison argument also implies a linear bound for the second fundamental form of self-shrinking surfaces under natural assumptions. As a consequence, translating solitons can be related to these self-shrinkers.
Cite
@article{arxiv.1412.4755,
title = {A maximum principle for self-shrinkers and some consequences},
author = {Antoine Song},
journal= {arXiv preprint arXiv:1412.4755},
year = {2014}
}