Pinching rigidity of minimal surfaces in spheres

TL;DR

This paper proves a pinching theorem related to the Simon conjecture for minimal surfaces in spheres, providing new proofs for certain cases using integral inequalities, advancing understanding of geometric rigidity.

Contribution

It establishes a pinching theorem for the Simon conjecture at s=3 and offers new proofs for s=1 and s=2 cases via Simons-type inequalities.

Findings

Proved a pinching theorem for s=3 case of the Simon conjecture.

Provided new proofs for s=1 and s=2 cases.

Utilized Simons-type integral inequalities to achieve these results.

Abstract

In this paper we give a pinching theorem of the Simon conjecture in the case s=3 and also give a new proof of the cases s=1 and s=2 by some Simons-type integral inequalities.