Errata and Addenda to: “Hydrodynamic Vortex on Surfaces” and “The motion of a vortex on a closed surface of constant negative curvature”

The paper’s Theorem 1 asserts exactly the two statements at issue—(a) critical points of the Robin function give equilibria with η=0, and (b) a vortex is at rest for every initial position iff the Robin function is constant and η is initially zero—derived from Gustafsson’s equations (concise form (22)–(23)) . The model’s solution proves (a) by direct substitution and (b) via a short ODE argument using (22) and then evaluating (23) at t=0 to force dR≡0, which is logically sound. The paper’s proof instead uses the L2 identity (19) for the velocity one-form U to deduce that U≡0 implies both dR≡0 and η≡0 . Thus, both are correct and reach the same conclusions with different proofs.