A1 Refereed original research article in a scientific journal
On the Hyperbolic Metric of Certain Domains
Authors: Hinkkanen Aimo, Vuorinen Matti
Publisher: Springer Science and Business Media Deutschland GmbH
Publication year: 2024
Journal: Computational Methods and Function Theory
Journal name in source: Computational Methods and Function Theory
eISSN: 2195-3724
DOI: https://doi.org/10.1007/s40315-023-00518-z
Web address : https://link.springer.com/article/10.1007/s40315-023-00518-z
Self-archived copy’s web address: https://arxiv.org/abs/2303.08238
Preprint address: https://arxiv.org/abs/2303.08238v1
We prove that if E is a compact subset of the unit disk D in the complex plane, if E contains a sequence of distinct points an≠ 0 for n≥ 1 such that lim n→∞an= 0 and for all n we have | an+1| ≥ | an| / 2 , and if G= D\ E is connected and 0 ∈ ∂G , then there is a constant c> 0 such that for all z∈ G we have λG(z) ≥ c/ | z| where λG(z) is the density of the hyperbolic metric in G.
© 2024, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
