On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913694353457152 |
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| author | Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan |
| author_facet | Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan |
| contents | One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and utilizing the approach we provided for constructing constant $p$-mean curvature surfaces, we have identified intriguing examples of such surfaces. Notably, we present a complete description of rotationally invariant surfaces of constant $p$-mean curvature and shed light on the geometric interpretation of the energy $E$ with a lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14697 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$ Chiu, Hung-Lin Lai, Sin-Hua Liu, Hsiao-Fan Differential Geometry 53A10, 53C42, 53C22, 34A26 One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and utilizing the approach we provided for constructing constant $p$-mean curvature surfaces, we have identified intriguing examples of such surfaces. Notably, we present a complete description of rotationally invariant surfaces of constant $p$-mean curvature and shed light on the geometric interpretation of the energy $E$ with a lower bound. |
| title | On Invariants of Constant $p$-Mean Curvature Surfaces in the Heisenberg Group $H_1$ |
| topic | Differential Geometry 53A10, 53C42, 53C22, 34A26 |
| url | https://arxiv.org/abs/2309.14697 |