Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866915051622891520 |
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| author | Ouyang, Charles Tamburelli, Andrea |
| author_facet | Ouyang, Charles Tamburelli, Andrea |
| contents | We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space $\mathbb{H}^{2,2}$. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of Hitchin representations along rays of quartic differentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_03499 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component Ouyang, Charles Tamburelli, Andrea Differential Geometry Geometric Topology We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space $\mathbb{H}^{2,2}$. In the process, we establish the closure in the space of projectivized geodesic currents of the space of flat metrics induced by holomorphic quartic differentials on a Riemann surface. As an application, we describe the behavior of the entropy of Hitchin representations along rays of quartic differentials. |
| title | Length spectrum compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2010.03499 |