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arXiv · 2606.02396

Existence of free boundary minimal disks in convex regions

Lorenzo Sarnataro·Douglas Stryker·Zhichao Wang·Xin Zhou
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Abstract

We show that any three-ball with mean convex boundary contains an embedded free boundary minimal disk. Moreover, when the three-ball is a strictly convex domain with nonnegative Ricci curvature (for instance, a compact convex domain in Euclidean three-space), we prove the existence of at least three embedded free boundary minimal disks. Our approach is based on a multiplicity-one theorem for the free boundary Simon-Smith min-max theory.

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Lorenzo Sarnataro, Douglas Stryker, Zhichao Wang, Xin Zhou. 2026-06-01. Existence of free boundary minimal disks in convex regions. https://arxiv.org/abs/2606.02396

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