HOLOMORPHIC VECTOR FIELDS WITH A BARYCENTRIC CONDITION

Dominique Cerveau, Julie Déserti, Alcides Lins Neto

correcthigh confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem 3.2 (Theorem A, 2‑chambar case) proves exactly what the candidate shows: for X1, X2 with the barycentric property, X2 = −X1, DX·X = 0, so the common foliation is by straight lines and, on each such line, the flows are translations. The candidate follows the same differentiation argument as the paper and reaches the same conclusions, adding only mild clarifications about leaf closures (as connected components of line∩U) and noting that only C1–C2 regularity is actually used. No substantive conflict.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The 2-chambar result is correctly proved, with a clear and concise argument hinging on differentiating the barycentric identity. The exposition is generally good, and the connection between the flow identity, the vanishing of DX·X, and straight-line trajectories is transparent. Minor clarifications about the closure of leaves (connected components) and minimal regularity would further strengthen readability and applicability.