Unbounded visibility domains: metric estimates and an application

Autor:	Banik, Annapurna, Bharali, Gautam
Rok vydání:	2024
Předmět:	Mathematics - Complex Variables Mathematics - Metric Geometry 32F45 32H25 32U05 (Primary) 32C25 32F18 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We give an explicit lower bound, in terms of the distance from the boundary, for the Kobayashi metric of a certain class of bounded pseudoconvex domains in $\mathbb{C}^n$ with $\mathcal{C}^2$-smooth boundary using the regularity theory for the complex Monge--Ampere equation. Using such an estimate, we construct a family of unbounded Kobayashi hyperbolic domains in $\mathbb{C}^n$ having a certain negative-curvature-type property with respect to the Kobayashi distance. As an application, we prove a Picard-type extension theorem for the latter domains. Comment: 15 pages; introduction significantly rewritten; some more details added to the proof of Theorem 1.2 (Theorem 1.4 in v1). Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.05704 Zobrazit plný text záznamu View this record from Arxiv