A Gap Theorem for Self-shrinkers of the Mean Curvature Flow in Arbitrary Codimension

TL;DR

This paper establishes a classification and gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension, focusing on those with bounded second fundamental form.

Contribution

It proves a new classification theorem for self-shrinkers with bounded curvature in any codimension, extending previous results.

Findings

Classification of self-shrinkers with |A|^2 ≤ 1

Establishment of a gap theorem in arbitrary codimension

Extension of mean curvature flow theory

Abstract

In this paper, we prove a classification theorem for self-shrinkers of the mean curvature flow with $|A|^2\le 1$ in arbitrary codimension. In particular, this implies a gap theorem for self-shrinkers in arbitrary codimension.