Conformally invariant metrics and lack of Hölder continuity




Kargar Rahim, Rainio Oona

PublisherSpringer

2024

Bulletin of the Malaysian Mathematical Sciences Society

Bull. Malays. Math. Sci. Soc.

48

47

2180-4206

DOIhttps://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.


Last updated on 2024-26-11 at 18:29