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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27337 |
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| _version_ | 1866913100682231808 |
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| author | Pu, Xingsi Wang, Lang |
| author_facet | Pu, Xingsi Wang, Lang |
| contents | In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains. As an application, we prove that a two dimensional bounded generic convex domain with piecewise $C^2$-smooth boundary that admits a finite volume quotient is biholomorphic to bidisk. Moreover, we show that any Teichm$\ddot{\operatorname{u}}$ller space $\mathcal{T}_g$ with $g\geq2$ can not be biholomorphic to a bounded generic domain with piecewise $C^2$-smooth boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27337 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometry of bounded generic domains with piecewise smooth boundary Pu, Xingsi Wang, Lang Complex Variables In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains. As an application, we prove that a two dimensional bounded generic convex domain with piecewise $C^2$-smooth boundary that admits a finite volume quotient is biholomorphic to bidisk. Moreover, we show that any Teichm$\ddot{\operatorname{u}}$ller space $\mathcal{T}_g$ with $g\geq2$ can not be biholomorphic to a bounded generic domain with piecewise $C^2$-smooth boundary. |
| title | Geometry of bounded generic domains with piecewise smooth boundary |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2604.27337 |