Extremal disc packings in compact hyperbolic surfaces
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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.
KeywordsRiemann surfaces Extremal k-packings Uniform Belyi functions Triangle groups
Mathematics Subject Classification30F10 52C26
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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