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Extremal disc packings in compact hyperbolic surfaces

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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.

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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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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, 28049, Madrid, Spain

    Ernesto Girondo

  2. Instituto de Ciencias Matemáticas ICMAT, Nicolás Cabrera 13-15, Campus de Cantoblanco, 28049, Madrid, Spain

    Ernesto Girondo

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  1. Ernesto Girondo
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Correspondence to Ernesto Girondo.

Additional information

This work was partially supported by the Grants MTM2012-31973 and MTM2016-79497-P of the Spanish MEyC and ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).

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Girondo, E. Extremal disc packings in compact hyperbolic surfaces. Rev Mat Complut 31, 467–478 (2018). https://doi.org/10.1007/s13163-017-0252-3

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  • DOI: https://doi.org/10.1007/s13163-017-0252-3

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