On the local systolic optimality of Zoll contact forms

Autor:	Abbondandolo, Alberto, Benedetti, Gabriele
Přispěvatelé:	Mathematics
Rok vydání:	2023
Předmět:	Mathematics - Symplectic Geometry FOS: Mathematics Symplectic Geometry (math.SG) Mathematics::Metric Geometry Mathematics::Differential Geometry Geometry and Topology Mathematics::Symplectic Geometry Analysis
Zdroj:	Geometric and Functional Analysis, 33(2), 299-363. Birkhauser Verlag Basel Abbondandolo, A & Benedetti, G 2023, ' On the local systolic optimality of Zoll contact forms ', Geometric and Functional Analysis, vol. 33, no. 2, pp. 299-363 . https://doi.org/10.1007/s00039-023-00624-z
ISSN:	1420-8970 1016-443X
Popis:	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. 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
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e61a1f4e602663bef522c6f2102ece7 https://doi.org/10.1007/s00039-023-00624-z Zobrazit plný text záznamu Full text from SpringerLink