Canonical Embeddings of Pairs of Arcs

Canonical Embeddings of Pairs of Arcs

We show that for given four points in the Riemann sphere and a given isotopy class of two disjoint arcs connecting these points in two pairs, there exists a unique configuration with the property that each arc is a hyperbolic geodesic segment in the complement of the other arc.

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Veröffentlicht in:Computational methods and function theory 2021-12, Vol.21 (4), p.825-830
Hauptverfasser: Bonk, Mario, Eremenko, Alexandre
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Riemann manifold
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Beschreibung
Zusammenfassung:We show that for given four points in the Riemann sphere and a given isotopy class of two disjoint arcs connecting these points in two pairs, there exists a unique configuration with the property that each arc is a hyperbolic geodesic segment in the complement of the other arc.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-021-00404-6