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Revista Matemática Complutense

, Volume 31, Issue 2, pp 467–478 | Cite as

Extremal disc packings in compact hyperbolic surfaces

  • Ernesto Girondo
Article
  • 105 Downloads

Abstract

We study packings of metric discs with respect to the canonical hyperbolic metric of a compact Riemann surface of genus greater than one. We find the maximum radius of a packing as a function of the genus and the number of discs and we investigate some properties of the surfaces that contain an extremal packing.

Keywords

Riemann surfaces Extremal k-packings Uniform Belyi functions Triangle groups 

Mathematics Subject Classification

30F10 52C26 

Notes

Acknowledgements

I am indebted to K. Böröczky and M. Conder for several valuable comments during the preparation of the article. Also to the reviewers for many interesting comments and questions that clearly improved the first version of the text.

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Copyright information

© Universidad Complutense de Madrid 2017

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  2. 2.Instituto de Ciencias Matemáticas ICMATMadridSpain

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