Blaschke-Lebesgue Problem On A Kind Of Convex Curves

We considered a kind of convex curves whose support function satisfies that:h(θ)+h(-θ) is constant in the paper, we call it X curve.In 4.1, we prove that the perimeter of x curves are the same; in 4.2, we prove that the Reuleaux triangle has the minimal area in x curves as the same in Blaschke-Lebesgue Theorem. we get conclusions above by using optimal control theory.