Conformally invariant metrics and lack of Hölder continuity
: Kargar Rahim, Rainio Oona
Publisher: Springer
: 2024
: Bulletin of the Malaysian Mathematical Sciences Society
: Bull. Malays. Math. Sci. Soc.
: 48
: 47
: 2180-4206
DOI: https://doi.org/10.1007/s40840-023-01648-2(external)
: https://link.springer.com/article/10.1007/s40840-023-01648-2(external)
: https://research.utu.fi/converis/portal/detail/Publication/381031473(external)
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.