The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914495436161024 |
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| author | Xin, Yue Li, Yan Hou, Bingzhe |
| author_facet | Xin, Yue Li, Yan Hou, Bingzhe |
| contents | In this paper, we study the right invariant metric $d_{H^{\infty}}$ on the analytic automorphism group $\rm{Aut}(\mathbb{D})$ of the unit open disk $\mathbb{D}$ induced by maximal modulus, that is, $d_{H^{\infty}}(φ, ψ)=\sup_{z\in\mathbb{D}}|φ(z)-ψ(z)|$ for any $φ, ψ\in \rm{Aut}(\mathbb{D})$. We give the explicit formula of the right invariant metric $d_{H^{\infty}}$ and characterize the almost regular Finsler geometric structure of $(\rm{Aut}(\mathbb{D}), d_{H^{\infty}})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19583 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus Xin, Yue Li, Yan Hou, Bingzhe Complex Variables Differential Geometry Group Theory Metric Geometry 53C60, 22F50, 54E35 In this paper, we study the right invariant metric $d_{H^{\infty}}$ on the analytic automorphism group $\rm{Aut}(\mathbb{D})$ of the unit open disk $\mathbb{D}$ induced by maximal modulus, that is, $d_{H^{\infty}}(φ, ψ)=\sup_{z\in\mathbb{D}}|φ(z)-ψ(z)|$ for any $φ, ψ\in \rm{Aut}(\mathbb{D})$. We give the explicit formula of the right invariant metric $d_{H^{\infty}}$ and characterize the almost regular Finsler geometric structure of $(\rm{Aut}(\mathbb{D}), d_{H^{\infty}})$. |
| title | The right invariant metric on the analytic automorphism group of the unit open disk induced by maximal modulus |
| topic | Complex Variables Differential Geometry Group Theory Metric Geometry 53C60, 22F50, 54E35 |
| url | https://arxiv.org/abs/2604.19583 |