Hyperbolic Distance versus Quasihyperbolic Distance in Plane Domains
| Autor: | Jeff Lindquist, David A. Herron |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Mathematics::Dynamical Systems Mathematics - Complex Variables 010102 general mathematics 02 engineering and technology General Medicine 021001 nanoscience & nanotechnology 01 natural sciences Domain (mathematical analysis) Metric space In plane Differential Geometry (math.DG) Euclidean geometry FOS: Mathematics Mathematics::Metric Geometry Primary: 30F45 30L99 Secondary: 51F99 30C62 0101 mathematics Complex Variables (math.CV) 0210 nano-technology Mathematics |
| DOI: | 10.48550/arxiv.2011.11016 |
| Popis: | We examine Euclidean plane domains with their hyperbolic or quasihyperbolic distance. We prove that the associated metric spaces are quasisymmetrically equivalent if and only if they are bi-Lipschitz equivalent. On the other hand, for Gromov hyperbolic domains, the two corresponding Gromov boundaries are always quasisymmetrically equivalent. Surprisingly, for any finitely connected hyperbolic domain, these two metric spaces are always quasiisometrically equivalent. We construct examples where the spaces are not quasiisometrically equivalent. |
| Databáze: | OpenAIRE |
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