Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866915182451621888 |
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| author | Sarnataro, Lorenzo Stryker, Douglas |
| author_facet | Sarnataro, Lorenzo Stryker, Douglas |
| contents | We prove the optimal $C^{1,1}$ regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescribed mean curvature in the round 3-sphere for an open dense set of prescribing functions with $L^{\infty}$ norm at most 0.547. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02722 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies Sarnataro, Lorenzo Stryker, Douglas Differential Geometry We prove the optimal $C^{1,1}$ regularity for minimizers of the prescribed mean curvature functional over isotopy classes. As an application, we find an embedded sphere of prescribed mean curvature in the round 3-sphere for an open dense set of prescribing functions with $L^{\infty}$ norm at most 0.547. |
| title | Optimal regularity for minimizers of the prescribed mean curvature functional over isotopies |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2304.02722 |