Article Dans Une Revue Geometry & Topology Monographs Année : 2025

CLOSED GEODESICS IN DILATION SURFACES

Résumé

We introduce the notion of exotic dilation surface, which provides a way to produce a weak form of compactification of the moduli space of dilation surfaces. This notion is devised to enable one to keep track of dynamical properties of their directional foliations along degenerating sequences. We derive from this construction a proof that every dilation surface contains a closed regular geodesic.

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hal-03427251 , version 1 (13-11-2021)

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Adrien Boulanger, Selim Ghazouani, Guillaume Tahar. CLOSED GEODESICS IN DILATION SURFACES. Geometry & Topology Monographs, 2025, 29 (4), pp.2217-2250. ⟨10.2140/gt.2025.29.2217⟩. ⟨hal-03427251⟩
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