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arXiv · 2206.08344

Strongly Goldilocks Domains, quantitative Visibility, and Applications

Nikolai Nikolov·Ahmed Yekta Ökten
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Abstract

In the last decade, G. Bharali and A. Zimmer defined a class of domains called Goldilocks domains and they showed that such a domain satisfies a visibility condition with respect to the Kobayashi extremal curves. Inspired by their construction, we define a subclass of Goldilocks domains called strongly Goldilocks domains and we prove a quantitative visibility result on strongly Goldilocks domains. Using our quantitative visibility result, we extend the Gehring-Hayman theorem on simply connected planar domains to strongly Goldilocks domains. As an application of our construction, we also give lower estimates to the Kobayashi distance.

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Nikolai Nikolov, Ahmed Yekta Ökten. 2022-06-16. Strongly Goldilocks Domains, quantitative Visibility, and Applications. https://doi.org/10.1016/j.jmaa.2024.128130

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