Abstract
Let \({{\mathcal {O}}}\) be a stable Riemann orbifold, that is, a closed 2-dimensional orbifold with nodes such that each connected component of the complement of the nodes has an analytically finite complex structure of hyperbolic type. We say that \({{\mathcal {O}}}\) is of Schottky type if there is a virtual noded Schottky group K such that \(\varOmega ^{ext}/K\) is isomorphic to it, where \(\varOmega ^{ext}\) is the extended domain of discontinuity of K. This is the same as saying that \({\mathcal {O}}\) is the conformal boundary at infinity of the hyperbolic 3-dimensional handlebody orbifold \({\mathbb {H}}^3/K\). In this paper we prove that the stable Riemann orbifolds of certain signature are of Schottky type.
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Acknowledgements
The authors would like to thank José-Luis Estévez for very useful discussions and to the referees for their commments and suggestions which permitted us to improve the paper. This work was partially supported by Projects MTM2017-89420-P and FONDECYT 1190001.
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Dedicated to the memory of Ignacio Garijo
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Díaz, R., Hidalgo, R.A. Stable Riemann orbifolds of Schottky type. RACSAM 115, 111 (2021). https://doi.org/10.1007/s13398-021-01052-0
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DOI: https://doi.org/10.1007/s13398-021-01052-0