Quantitative localization and comparison of invariant distances of domains in $\mathbb C^n$

Nikolai Nikolov; Pascal J. Thomas

Quantitative localization and comparison of invariant distances of domains in $\mathbb C^n$

Complex Variables 2024-05-28 v3

Authors: Nikolai Nikolov , Pascal J. Thomas

Abstract

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 $1$ .

Keywords

invariant distances kobayashi distance domains in $\mathbb C^n$ quantitative localization boundary point sharp estimates

Cite

@article{arxiv.2109.01944,
  title  = {Quantitative localization and comparison of invariant distances of domains in $\mathbb C^n$},
  author = {Nikolai Nikolov and Pascal J. Thomas},
  journal= {arXiv preprint arXiv:2109.01944},
  year   = {2024}
}

Comments

v2: Results about ratio of invariant distances and some references have been added, some proofs have been streamlined. v3: Major revision. To appear in J. Geom. Anal

Quantitative localization and comparison of invariant distances of domains in $\mathbb C^n$

Abstract

Keywords

Cite

Comments

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