SMOOTH ORBIT EQUIVALENCE RIGIDITY FOR DISSIPATIVE GEODESIC FLOWS

Javier Echevarría Cuesta

correctmedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves the metric–conformal rigidity and the 1-form statement under the closedness hypothesis using period-matrix preservation via a transport/currents pairing, Torelli, lifting to finite covers, and a Livšic-based argument for the 1-forms (Theorem 1.3 and Proposition 4.7 in the paper). The candidate’s outline matches the period-matrix/Torelli strategy, but its treatment of the 1-form part makes a false inference (d⋆θ = 0 ⇒ divµa E = 0) and misstates how θ transforms under conformal fibre scaling; it also invokes an unnecessary and unsubstantiated s-injectivity claim. The paper’s argument remains correct and complete, while the candidate’s proof is flawed in the “moreover” clause (even though the final conclusion coincides).

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper establishes a robust rigidity theorem for Gaussian thermostats with negative thermostat curvature under smooth orbit equivalence isotopic to the identity. The approach—transport/currents technology for preserving periods, Torelli for complex structures, and a careful Livšic-based argument for the 1-form—is executed cleanly and addresses the dissipative complications head-on. The results appear correct and significant; suggested revisions are minor clarifications to aid readability.