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1 February 2021 On the minimal diameter of closed hyperbolic surfaces
Thomas Budzinski, Nicolas Curien, Bram Petri
Duke Math. J. 170(2): 365-377 (1 February 2021). DOI: 10.1215/00127094-2020-0083

Abstract

We prove that the minimal diameter of a closed orientable hyperbolic surface of genus g is asymptotic to logg as g. The proof relies on a random construction, which we analyze using lattice-point counting theory and the exploration of random trivalent graphs.

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Thomas Budzinski. Nicolas Curien. Bram Petri. "On the minimal diameter of closed hyperbolic surfaces." Duke Math. J. 170 (2) 365 - 377, 1 February 2021. https://doi.org/10.1215/00127094-2020-0083

Information

Received: 30 September 2019; Revised: 11 June 2020; Published: 1 February 2021
First available in Project Euclid: 10 December 2020

Digital Object Identifier: 10.1215/00127094-2020-0083

Subjects:
Primary: 05C80
Secondary: 30F10, 57M15

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 2 • 1 February 2021
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