Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula --
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916865071120384 |
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| author | Miyachi, Hideki |
| author_facet | Miyachi, Hideki |
| contents | In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichmüller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichmüller space, as well as a Teichmüller-theoretic interpretation of the mean value theorem for pluriharmonic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula -- Miyachi, Hideki Complex Variables Geometric Topology 32G05, 32G15, 32U35, 57M50 In this paper, we establish the Poisson integral formula for bounded pluriharmonic functions on the Teichmüller space of analytically finite Riemann surfaces of type $(g,m)$ with $2g-2+m>0$. We also discuss a version of the F. and M. Riesz theorem concerning the value distribution of plurisubharmonic functions on the Teichmüller space, as well as a Teichmüller-theoretic interpretation of the mean value theorem for pluriharmonic functions. |
| title | Bounded Pluriharmonic Functions and Holomorphic Functions on Teichmüller Space II -- Poisson integral formula -- |
| topic | Complex Variables Geometric Topology 32G05, 32G15, 32U35, 57M50 |
| url | https://arxiv.org/abs/2507.19930 |