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arXiv · 1912.04187

On the local systolic optimality of Zoll contact forms

Alberto Abbondandolo·Gabriele Benedetti
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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.

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Alberto Abbondandolo, Gabriele Benedetti. 2019-12-09. On the local systolic optimality of Zoll contact forms. https://arxiv.org/abs/1912.04187

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