Self-Adjoint Laplacians on Partially and Generalized Hyperbolic Attractors

Shayan Alikhanloo, Michael Hinz

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 closability and the existence of the self-adjoint generator using only equivalence of leafwise conditional measures to Riemannian volume and a superposition/disintegration argument; no differentiability of the conditional densities is required. The model’s proof inserts an integration-by-parts step on plaques that needs ∇ log ρB to exist and be bounded, which is not assumed (µ ∈ Mac_bd only gives two-sided L∞ bounds). Hence the model’s argument has a technical gap, while the paper’s argument is complete.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper’s main theorem is correct under its stated hypotheses. The proof strategically avoids unnecessary smoothness of conditional densities by employing disintegration and known closability results for plaque-wise Dirichlet integrals combined via a superposition argument. The exposition is generally clear and well referenced to standard Dirichlet form literature. Minor presentational refinements would aid readability.