# A rigidity theorem on the second fundamental form for self-shrinkers

## TL;DR

This paper extends a rigidity theorem for self-shrinkers by relaxing the integral condition on the second fundamental form to a finite constant, broadening the class of self-shrinkers satisfying the theorem.

## Contribution

It generalizes previous rigidity results by replacing the integral bound with a finite constant condition on the second fundamental form.

## Key findings

- Rigidity theorem holds under finite constant bound
- Broader class of self-shrinkers characterized
- Extension of previous integral condition results

## Abstract

In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).