arXiv:2410.00642 Abstract | arXiv Analytics

arXiv:2410.00642 [math.DS]Abstract References Reviews Resources

Sub-actions for geodesic flows on locally CAT(-1) spaces

David Constantine, Elvin Shrestha, Yandi Wu

Published 2024-10-01Version 1

We extend a result of Lopes and Thieullen 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.

Comments: 56 pages, 6 figures

Categories: math.DS, math.MG

Subjects: 37D40

Keywords: locally cat, geodesic flow, sub-actions, smooth anosov flows, volume rigidity theorem

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