Conformally invariant metrics and lack of Hölder continuity
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911764142096384 |
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| author | Kargar, Rahim Rainio, Oona |
| author_facet | Kargar, Rahim Rainio, Oona |
| contents | 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 Hölder continuous with respect to the hyperbolic metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11588 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Conformally invariant metrics and lack of Hölder continuity Kargar, Rahim Rainio, Oona Complex Variables Metric Geometry 51M09, 30F45 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 Hölder continuous with respect to the hyperbolic metric. |
| title | Conformally invariant metrics and lack of Hölder continuity |
| topic | Complex Variables Metric Geometry 51M09, 30F45 |
| url | https://arxiv.org/abs/2304.11588 |