Dido's Problem and the Curvature-Variation Energy: Proof of the Least-Variation Conjecture and a Local Stability Theorem
Original effort. For a closed curve on a Riemannian surface, the curvature-variation energy J vanishes exactly when geodesic curvature is constant. This note proves that a smoothly attained fixed-length area maximizer has constant geodesic curvature, hence J = 0, and a local quantitative stability theorem.