Quantitative Localization and Comparison of Invariant Distances of Domains in $$\mathbb C^n

We obtain explicit bounds on the difference and ratio between "local" and "global" Kobayashi distances in a domain of $\mathbb C^n$ as the points go toward a boundary point with appropriate geometric properties. We use this for the global comparison of various invariant distances...

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Bibliographic Details
Published inThe Journal of geometric analysis Vol. 33; no. 1
Main Authors Nikolov, Nikolai, Thomas, Pascal J.
Format Journal Article
LanguageEnglish
Published Springer 01.01.2023
Subjects
Complex Variables
Mathematics
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Summary:We obtain explicit bounds on the difference and ratio between "local" and "global" Kobayashi distances in a domain of $\mathbb C^n$ as the points go toward a boundary point with appropriate geometric properties. We use this for the global comparison of various invariant distances. We provide some sharp estimates in dimension $1$.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01086-9