Unbounded visibility domains: metric estimates and an application
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918077271113728 |
|---|---|
| author | Banik, Annapurna Bharali, Gautam |
| author_facet | Banik, Annapurna Bharali, Gautam |
| contents | 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, among other tools, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05704 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unbounded visibility domains: metric estimates and an application Banik, Annapurna Bharali, Gautam Complex Variables Metric Geometry 32F45, 32H25, 32U05 (Primary) 32C25, 32F18 (Secondary) 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, among other tools, 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. |
| title | Unbounded visibility domains: metric estimates and an application |
| topic | Complex Variables Metric Geometry 32F45, 32H25, 32U05 (Primary) 32C25, 32F18 (Secondary) |
| url | https://arxiv.org/abs/2405.05704 |