On the local systolic optimality of Zoll contact forms

Abstract We prove a normal form for contact forms close to Zoll one and deduce that on any closed manifold are local maximizers of the systolic ratio. Corollaries this result are: (1) sharp inequalities Riemannian Finsler metrics ones, (2) perturbative case conjecture Viterbo symplectic capacity convex bodies, (3) generalization Gromov’s non-squeezing theorem in intermediate dimensions symplectomorphisms linear ones.