THE ECH CAPACITIES FOR THE ROTATING KEPLER PROBLEM

Amin Mohebbi

correctmedium confidence

Category: Not specified
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper proves F(r1) = Area(K_bc − ω1)/Area(ω1) ≤ 1/2 for c ≤ −3/2 by an explicit integral followed by a monotonicity-in-R argument (Theorem 5.2), and checks the equality case at c = −3/2; the candidate solution establishes the same inequality via a shorter, exact endpoint identity, yielding the closed form F(r1) = 1/2 − ((r2 − 2 r1)^2)/(2 r1^2). Both approaches are consistent with the paper’s set-up for K_bc and its first weight W1, and both support the intended conclusion that W1 is the largest weight. The model’s derivation is strictly stronger (it gives an exact formula), while the paper’s proof is more cumbersome but still correct.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The core inequality F ≤ 1/2 for c ≤ −3/2 is established correctly from the SCTD geometry and an explicit integral, and the equality case is checked. The manuscript’s argument is somewhat longer than necessary; a short endpoint-identity argument yields an exact closed form and would improve readability. The intended corollary—that W1 is the largest weight—is standard but should be stated and derived explicitly. Some displays (e.g., c(r1)) would benefit from clearer notation.