Area Rigidity for the Regular Representation of Surface Groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908505424789504 |
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| author | Caniato, Riccardo Li, Xingzhe Song, Antoine |
| author_facet | Caniato, Riccardo Li, Xingzhe Song, Antoine |
| contents | Let $\tildeΣ$ be the universal cover of a closed surface $Σ$ of genus at least $2$. We characterize all equivariantly area-minimizing maps from $\tildeΣ$ to a Hilbert sphere, which are equivariant with respect to an isometric action of $π_1(Σ)$ weakly equivalent to the regular representation. As part of our proof, we classify all minimal surfaces in Hilbert spheres with constant negative Gaussian curvature. This builds on earlier results of E. Calabi, K. Kenmotsu, R. Bryant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Area Rigidity for the Regular Representation of Surface Groups Caniato, Riccardo Li, Xingzhe Song, Antoine Differential Geometry Representation Theory Let $\tildeΣ$ be the universal cover of a closed surface $Σ$ of genus at least $2$. We characterize all equivariantly area-minimizing maps from $\tildeΣ$ to a Hilbert sphere, which are equivariant with respect to an isometric action of $π_1(Σ)$ weakly equivalent to the regular representation. As part of our proof, we classify all minimal surfaces in Hilbert spheres with constant negative Gaussian curvature. This builds on earlier results of E. Calabi, K. Kenmotsu, R. Bryant. |
| title | Area Rigidity for the Regular Representation of Surface Groups |
| topic | Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2508.19480 |