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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08228 |
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| _version_ | 1866917073260642304 |
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| author | Mazurowski, Liam Zhou, Xin |
| author_facet | Mazurowski, Liam Zhou, Xin |
| contents | Assume $h$ is a positive function on the unit three-sphere which satisfies the pinching condition $h < h_0 \approx 0.547$. We prove the existence of at least two embedded two-spheres with prescribed mean curvature $h$. The same result holds for sign-changing functions $h$ satisfying $\vert h\vert < h_0$ under a mild assumption on the zero set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature Mazurowski, Liam Zhou, Xin Differential Geometry 53A10 Assume $h$ is a positive function on the unit three-sphere which satisfies the pinching condition $h < h_0 \approx 0.547$. We prove the existence of at least two embedded two-spheres with prescribed mean curvature $h$. The same result holds for sign-changing functions $h$ satisfying $\vert h\vert < h_0$ under a mild assumption on the zero set. |
| title | Pairs of Embedded Spheres with Pinched Prescribed Mean Curvature |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/2511.08228 |