On the Gauss Map of Anisotropic Minimal Surfaces and applications to the Morse Index estimates
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917881175867392 |
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| author | Inoue, Toshimi |
| author_facet | Inoue, Toshimi |
| contents | In the paper, we study the Gauss map of a completely immersed anisotropic minimal surface with respect to convex parametric integrand in $\mathbb{R}^3$. By a local analysis, we prove the discreteness of the critical set of the Gauss map of an anisotropic minimal surface. In particular, we may consider the Gauss map as a branched covering map from an anisotropic minimal surface to the unit sphere. As a consequence, we may obtain an upper and a lower estimate for the Morse index of an anisotropic minimal surface by applying some conformal geometric technics to the Gauss map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Gauss Map of Anisotropic Minimal Surfaces and applications to the Morse Index estimates Inoue, Toshimi Differential Geometry In the paper, we study the Gauss map of a completely immersed anisotropic minimal surface with respect to convex parametric integrand in $\mathbb{R}^3$. By a local analysis, we prove the discreteness of the critical set of the Gauss map of an anisotropic minimal surface. In particular, we may consider the Gauss map as a branched covering map from an anisotropic minimal surface to the unit sphere. As a consequence, we may obtain an upper and a lower estimate for the Morse index of an anisotropic minimal surface by applying some conformal geometric technics to the Gauss map. |
| title | On the Gauss Map of Anisotropic Minimal Surfaces and applications to the Morse Index estimates |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.20502 |