Area rigidity for the equatorial disk in the ball

Abstract

It is proved by Brendle in [4] that the equatorial disk $D^k$ has least area among $k$-dimensional free boundary minimal surfaces in the Euclidean ball $B^n$. By comparing the excess of free boundary minimal surfaces with the excess of the associated cones over the boundary, we prove the existence of a gap for the area.

12 pages. Revised. Lemma 3.1 is replaced by Theorem 3.1. Lemma 3.3 added