On the local systolic optimality of Zoll contact forms
Symplectic Geometry
2023-12-15 v3
Abstract
We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this result are: (i) sharp local systolic inequalities for Riemannian and Finsler metrics close to Zoll ones, (ii) the perturbative case of a conjecture of Viterbo on the symplectic capacity of convex bodies, (iii) a generalization of Gromov's non-squeezing theorem in the intermediate dimensions for symplectomorphisms that are close to linear ones.
Keywords
Cite
@article{arxiv.1912.04187,
title = {On the local systolic optimality of Zoll contact forms},
author = {Alberto Abbondandolo and Gabriele Benedetti},
journal= {arXiv preprint arXiv:1912.04187},
year = {2023}
}
Comments
63 pages; v3: perturbative version of the Viterbo conjecture now proven for arbitrary symplectic capacities, added more properties to the normal form, added a statement on the local rigidity of Zoll contact forms