A remark on a curvature gap for minimal surfaces in the ball

TL;DR

This paper generalizes a previous curvature characterization of certain minimal surfaces in the 3D ball to higher codimensions, providing new geometric insights into free boundary minimal surfaces.

Contribution

It extends earlier curvature pinching conditions to higher codimension free boundary minimal surfaces, broadening the understanding of their geometric properties.

Findings

Characterization of equatorial disk and critical catenoid in higher codimension

Extension of curvature pinching conditions

New geometric criteria for free boundary minimal surfaces

Abstract

We extend to higher codimension earlier characterization of the equatorial disk and the critical catenoid by a pinching condition on the length of their second fundamental form among free boundary minimal surfaces in the three dimensional Euclidean ball due to L. Ambrozio and I. Nunes.