A1 Refereed original research article in a scientific journal
Conformally invariant metrics and lack of Hölder continuity
Authors: Kargar Rahim, Rainio Oona
Publisher: Springer
Publication year: 2024
Journal: Bulletin of the Malaysian Mathematical Sciences Society
Journal acronym: Bull. Malays. Math. Sci. Soc.
Article number: 48
Volume: 47
eISSN: 2180-4206
DOI: https://doi.org/10.1007/s40840-023-01648-2
Web address : https://link.springer.com/article/10.1007/s40840-023-01648-2
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/381031473
The modulus metric between two points in a subdomain of Rn, n ≥ 2, is defined in terms of moduli of curve families joining the boundary of the domain with a continuum connecting the two points. This metric is one of the conformally invariant hyperbolictype metrics that have become a standard tool in geometric function theory. We prove that the modulus metric is not Hölder continuous with respect to the hyperbolic metric.
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