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Geometric filling curves on punctured surfaces

Part of: Global differential geometry Riemann surfaces Deformations of analytic structures

Published online by Cambridge University Press:  15 December 2022

Nhat Minh Doan Open the ORCID record for Nhat Minh Doan [Opens in a new window]
Nhat Minh Doan*
Affiliation:
Department of Mathematics, University of Luxembourg, Esch-sur-Alzette, Luxembourg and Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
*
E-mail: dnminh@math.ac.vn
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Abstract

This paper is about a type of quantitative density of closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds on the length of the shortest closed geodesic and the shortest doubly truncated orthogeodesic that are $\varepsilon$-dense on a given compact set on the surface.

Keywords

hyperbolic surfacesclosed geodesicsgeometric fillingcurves

MSC classification

Primary: 30F10: Compact Riemann surfaces and uniformization
Secondary: 32G15: Moduli of Riemann surfaces, Teichmüller theory 53C22: Geodesics
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 2 , May 2023 , pp. 383 - 400
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

*

Research supported by FNR PRIDE15/10949314/GSM.

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