A maximum principle for self-shrinkers and some consequences

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.

Cited by in corpus (2)

• Asymptotic structure of self-shrinkers
• Geometry of Two-dimensional Self-shrinkers