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arXiv · 1409.1632

Uniqueness theorems for free boundary minimal disks in space forms

Ailana Fraser·Richard Schoen
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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.

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Ailana Fraser, Richard Schoen. 2014-09-04. Uniqueness theorems for free boundary minimal disks in space forms. https://arxiv.org/abs/1409.1632

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