Symmetric differentials and jets extension of $L^2$ holomorphic functions II: Explicit form
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912716144246784 |
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| author | Lee, Seungjae Seo, Aeryeong |
| author_facet | Lee, Seungjae Seo, Aeryeong |
| contents | For a symmetric differential on the compact quotient $Σ= \mathbb{B}^n / Γ$ of the complex unit ball $\mathbb{B}^n \subset \mathbb{C}^n$ by a discrete subgroup $Γ\subset \mathrm{Aut}(\mathbb{B}^n)$, there exists a corresponding weighted $L^2$-holomorphic function on $(\mathbb{B}^n \times \mathbb{B}^n)/Γ$, where $Γ$ acts diagonally on $\mathbb{B}^n \times \mathbb{B}^n$. In this paper, we give an explicit description of this correspondence and derive several applications based on its explicit form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetric differentials and jets extension of $L^2$ holomorphic functions II: Explicit form Lee, Seungjae Seo, Aeryeong Complex Variables Differential Geometry 32A36 For a symmetric differential on the compact quotient $Σ= \mathbb{B}^n / Γ$ of the complex unit ball $\mathbb{B}^n \subset \mathbb{C}^n$ by a discrete subgroup $Γ\subset \mathrm{Aut}(\mathbb{B}^n)$, there exists a corresponding weighted $L^2$-holomorphic function on $(\mathbb{B}^n \times \mathbb{B}^n)/Γ$, where $Γ$ acts diagonally on $\mathbb{B}^n \times \mathbb{B}^n$. In this paper, we give an explicit description of this correspondence and derive several applications based on its explicit form. |
| title | Symmetric differentials and jets extension of $L^2$ holomorphic functions II: Explicit form |
| topic | Complex Variables Differential Geometry 32A36 |
| url | https://arxiv.org/abs/2511.14177 |