Uniqueness theorems for free boundary minimal disks in space forms
Differential Geometry
2018-11-28 v2
Abstract
We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. Nitsche and R. Souam.
Keywords
Cite
@article{arxiv.1409.1632,
title = {Uniqueness theorems for free boundary minimal disks in space forms},
author = {Ailana Fraser and Richard Schoen},
journal= {arXiv preprint arXiv:1409.1632},
year = {2018}
}
Comments
A misprint was corrected and a minor amplification of the argument of the proof of Theorem 2.2 was given. Thanks to Ivan Solonenko for pointing to these issues in the paper