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arXiv · 2304.11588

Conformally invariant metrics and lack of H\"older continuity

Rahim Kargar·Oona Rainio
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Abstract

The modulus metric between two points in a subdomain of $\mathbb{R}^n, n\ge 2,$ 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 hyperbolic type metrics, which have become a standard tool in geometric function theory. We prove that the modulus metric is not H\"{o}lder continuous with respect to the hyperbolic metric.

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Rahim Kargar, Oona Rainio. 2023-04-23. Conformally invariant metrics and lack of H\"older continuity. https://arxiv.org/abs/2304.11588

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