2410.00642
Sub-actions for geodesic flows on locally CAT(-1) spaces
David Constantine, Elvin Shrestha, Yandi Wu
correcthigh confidence
- Category
- Not specified
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves the sub-action theorem for geodesic flows on compact locally CAT(-1) spaces by discretizing via Markov sections, constructing a sub-action for the return map, and then extending it to the flow with a careful smoothing/inductive scheme. The candidate solution proves the same statement by invoking a positive Livšic/cohomological inequality on an irreducible SFT, then lifting to the flow with a bump-function construction. Both routes are valid; the candidate’s approach is shorter but leaves technical regularity (Hölder) details and irreducibility assumptions implicit.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The work adapts sub-action theory from smooth Anosov flows to geodesic flows in locally CAT(-1) spaces, providing a new tool with a concrete rigidity application. The discretization and extension arguments are technically careful and correctly adapted to the metric setting. While the contribution is specialized, it is solid and of interest to researchers in dynamics and rigidity. Minor expository improvements would further aid readability.