Existence of free boundary minimal disks in convex regions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917556066975744 |
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| author | Sarnataro, Lorenzo Stryker, Douglas Wang, Zhichao Zhou, Xin |
| author_facet | Sarnataro, Lorenzo Stryker, Douglas Wang, Zhichao Zhou, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_02396 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of free boundary minimal disks in convex regions Sarnataro, Lorenzo Stryker, Douglas Wang, Zhichao Zhou, Xin Differential Geometry Analysis of PDEs Geometric Topology 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. |
| title | Existence of free boundary minimal disks in convex regions |
| topic | Differential Geometry Analysis of PDEs Geometric Topology |
| url | https://arxiv.org/abs/2606.02396 |