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Sub-actions for geodesic flows on locally CAT(
$-1$) spaces
- Part of
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- Journal:
- Ergodic Theory and Dynamical Systems , First View
- Published online by Cambridge University Press:
- 06 August 2025, pp. 1-44
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- Article
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We extend a result of Lopes and Thieullen [Sub-actions for Anosov flows. Ergod. Th. & Dynam. Sys. 25(2) (2005), 605–628] on sub-actions for smooth Anosov flows to the setting of geodesic flow on locally CAT(
$-1$) spaces. This allows us to use arguments originally due to Croke and Dairbekov to prove a volume rigidity theorem for some interesting locally CAT(
$-1$) spaces, including quotients of Fuchsian buildings and surface amalgams.
