Asymptotic behaviour of the Bergman invariant and Kobayashi metric on exponentially flat infinite type domains
| Autor: | Jaiswal, Ravi Shankar |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We prove the nontangential asymptotic limits of the Bergman canonical invariant, Ricci and Scalar curvatures of the Bergman metric, as well as the Kobayashi--Fuks metric, at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in $\mathbb{C}^{n + 1}, \, n \in \mathbb{N}$. Additionally, we establish the nontangential asymptotic limit of the Kobayashi metric at exponentially flat infinite type boundary points of smooth bounded domains in $\mathbb{C}^{n + 1}, \, n \in \mathbb{N}$. We first show that these objects satisfy appropriate localizations and then utilize the method of scaling to complete the proofs. Comment: 23 pages, comments welcome |
| Databáze: | arXiv |
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