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Closed geodesics in
dilation surfaces
Adrien Boulanger, Selim Ghazouani and Guillaume Tahar |
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Geometry & Topology 29 (2025) 2217–2250
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Abstract |
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We prove that directions of closed geodesics in every dilation surface form a dense subset of the circle. The proof draws on a study of the degenerations of the Delaunay triangulation of dilation surfaces under the action of Teichmüller flow in the moduli space. |
Keywords
dilation surface, closed geodesic, Delaunay triangulation
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Mathematical Subject Classification
Primary: 37E35
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References |
Publication
Received: 24 August 2023
Revised: 16 May 2024
Accepted: 6 July 2024
Published: 27 June 2025
Proposed: Benson Farb
Seconded: Mladen Bestvina, David Fisher
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Authors |
| Adrien Boulanger | |
| Institut Mathématique de Marseille,
CNRS Aix-Marseille Université Marseille France |
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| Selim Ghazouani | |
| Department of Mathematics University College London London United Kingdom |
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| Guillaume Tahar | |
| Faculty of Mathematics and Computer
Science Beijing Institute of Mathematical Sciences and Applications Beijing China |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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