On the properness of $p$-conformal energy on the Teichmüller space of a Riemann surface
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908514923839488 |
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| author | Alaqad, Hala Gong, Jianhua Martin, Gaven Yao, Cong |
| author_facet | Alaqad, Hala Gong, Jianhua Martin, Gaven Yao, Cong |
| contents | We establish that the $p$-conformal energy, $p\geq 1$, defined by the $L^p$-norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller space of Riemann surfaces of a fixed genus. This result is an application of a result herein identifying explicitly both the unique extremal mappings of finite distortion between hyperbolic annuli of given modulus, and their $p$-conformal energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01841 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the properness of $p$-conformal energy on the Teichmüller space of a Riemann surface Alaqad, Hala Gong, Jianhua Martin, Gaven Yao, Cong Complex Variables 30C We establish that the $p$-conformal energy, $p\geq 1$, defined by the $L^p$-norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller space of Riemann surfaces of a fixed genus. This result is an application of a result herein identifying explicitly both the unique extremal mappings of finite distortion between hyperbolic annuli of given modulus, and their $p$-conformal energy. |
| title | On the properness of $p$-conformal energy on the Teichmüller space of a Riemann surface |
| topic | Complex Variables 30C |
| url | https://arxiv.org/abs/2509.01841 |