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The maximal injectivity radius of hyperbolic surfaces with geodesic boundary

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Abstract

We give sharp upper bounds on the injectivity radii of complete hyperbolic surfaces of finite area with some geodesic boundary components. The given bounds are over all such surfaces with any fixed topology; in particular, boundary lengths are not fixed. This extends the first author’s earlier result to the with-boundary setting. In the second part of the paper we comment on another direction for extending this result, via the systole of loops function.

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Acknowledgements

Sects. 1 and 3 of this paper are adapted from the second author’s 2018 University of Pittsburgh Ph.D. thesis, directed by the first author. We thank thesis committee members Tom Hales, Chris Lennard, and Matt Stover for helpful feedback. We are also grateful to the referee for helpful comments and references.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

    Jason DeBlois

  2. Catalyte, Denver, CO, USA

    Kim Romanelli

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  1. Jason DeBlois
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  2. Kim Romanelli
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Correspondence to Jason DeBlois.

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DeBlois, J., Romanelli, K. The maximal injectivity radius of hyperbolic surfaces with geodesic boundary. Geom Dedicata 210, 103–129 (2021). https://doi.org/10.1007/s10711-020-00535-5

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