Classification of branched Willmore spheres
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913408403636224 |
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| author | Martino, Dorian |
| author_facet | Martino, Dorian |
| contents | Given a branched Willmore immersion from a closed Riemann surface, we show that Bryant's quartic is holomorphic. Consequently, this quartic vanishes when the underlying surface is a sphere and we obtain the full classification of branched Willmore spheres. To do so, we show that the asymptotic expansion in the $C^2$-topology of the conformal Gauss map at a branched point is a null straight line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of branched Willmore spheres Martino, Dorian Differential Geometry Given a branched Willmore immersion from a closed Riemann surface, we show that Bryant's quartic is holomorphic. Consequently, this quartic vanishes when the underlying surface is a sphere and we obtain the full classification of branched Willmore spheres. To do so, we show that the asymptotic expansion in the $C^2$-topology of the conformal Gauss map at a branched point is a null straight line. |
| title | Classification of branched Willmore spheres |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2306.07965 |