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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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Canonical Embeddings of Pairs of Arcs

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-021-00404-6
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Dec 1, 2021

Keywords: Conformal map; Hyperbolic metric; Conic singularity; Primary 30F45; 60J67; 81T40

References

  • Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
    Eremenko, A; Gabrielov, A