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Geometric filling curves on punctured surfaces

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

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.

References

Basmajian, A., The orthogonal spectrum of a hyperbolic manifold, Am. J. Math. 115(5) (1993), 1139–1159.CrossRefGoogle Scholar
Basmajian, A., Universal length bounds for non-simple closed geodesics on hyperbolic surfaces, J. Topol. 6(2) (2013), 513–524.CrossRefGoogle Scholar
Basmajian, A., Parlier, H. and Souto, J., Geometric filling curves on surfaces, Bull. London Math. Soc. 49(4) (2017), 660–669.CrossRefGoogle Scholar
Beardon, A. F., The geometry of discrete groups, vol. 91 (Springer Science & Business Media, New York, 2012).Google Scholar
Buser, P., Geometry and spectra of compact riemann surfaces (Springer Science & Business Media, Boston, MA, 2010).CrossRefGoogle Scholar
Chang, H.-C. and de Mesmay, A., Tightening curves on surfaces monotonically with applications, in Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SIAM, 2020), 747–766.CrossRefGoogle Scholar
Katok, A. and Hasselblatt, B., Introduction to the modern theory of dynamical systems, vol. 54 (Cambridge University Press, Cambridge, 1995).CrossRefGoogle Scholar
McShane, G., Simple geodesics and a series constant over teichmuller space, Inventiones Mathematicae 132(3) (1998), 607–632.CrossRefGoogle Scholar
Parlier, H., Geodesic and orthogeodesic identities on hyperbolic surfaces, arXiv preprint arXiv:2004.09078 (2020).Google Scholar