Geodesic
Closed geodesics in dilation surfaces
Boulanger, Adrien1 ; Ghazouani, Selim2 ; Tahar, Guillaume3
1Institut Mathématique de Marseille, CNRS, Aix-Marseille Université, Marseille, France
2Department of Mathematics, University College London, London, United Kingdom
3Faculty of Mathematics and Computer Science, Beijing Institute of Mathematical Sciences and Applications, Beijing, China
Geometry & topology, Tome 29 (2025) no. 4, pp. 2217-2250
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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.

DOI : 10.2140/gt.2025.29.2217
Keywords: dilation surface, closed geodesic, Delaunay triangulation

Boulanger, Adrien  1   ; Ghazouani, Selim  2   ; Tahar, Guillaume  3

1 Institut Mathématique de Marseille, CNRS, Aix-Marseille Université, Marseille, France
2 Department of Mathematics, University College London, London, United Kingdom
3 Faculty of Mathematics and Computer Science, Beijing Institute of Mathematical Sciences and Applications, Beijing, China 
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Boulanger, Adrien; Ghazouani, Selim; Tahar, Guillaume. Closed geodesics in dilation surfaces. Geometry & topology, Tome 29 (2025) no. 4, pp. 2217-2250. doi: 10.2140/gt.2025.29.2217

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