Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917009140219904 |
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| author | Ferro, Marcelo Lopes Corro, Armando M. V. |
| author_facet | Ferro, Marcelo Lopes Corro, Armando M. V. |
| contents | In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature Ferro, Marcelo Lopes Corro, Armando M. V. Differential Geometry Geometric Topology In this work, we provide a local classification of certain special classes of surfaces determined by the prescription of the radial mean curvature in terms of the height and angle functions. Moreover, we introduce a special class of hypersurfaces, and we also provide a local classification of these three-dimensional hypersurfaces whose second mean curvature vanishes. Finally, we present a recursive method for constructing such hypersurfaces, extending the same curvature prescription approach to higher dimensions. |
| title | Surfaces and Hypersurfaces with Prescribed Radial Mean Curvature |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2510.11669 |