Almost-Fuchsian representations in PU(2,1)
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915822253899776 |
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| author | Bronstein, Samuel |
| author_facet | Bronstein, Samuel |
| contents | In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1) |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16261 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost-Fuchsian representations in PU(2,1) Bronstein, Samuel Differential Geometry Functional Analysis Geometric Topology 53C43, 53C42, 58J60, 53C07 In this paper, we study nonmaximal representations of surface groups in PU(2,1). In genus large enough, we show the existence of convex-cocompact representations of non-maximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and almost totally geodesic. These examples can be obtained for any Toledo invariant of the form 2-2g +2/3 d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1) |
| title | Almost-Fuchsian representations in PU(2,1) |
| topic | Differential Geometry Functional Analysis Geometric Topology 53C43, 53C42, 58J60, 53C07 |
| url | https://arxiv.org/abs/2411.16261 |