Asymptotic equivalence of symplectic capacities
Efim D. Gluskin
Tel Aviv University, IsraelYaron Ostrover
Tel Aviv University, Israel
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Abstract
A long-standing conjecture states that all normalized symplectic capacities coincide on the class of convex subsets of . In this note we focus on an asymptotic (in the dimension) version of this conjecture, and show that when restricted to the class of centrally symmetric convex bodies in , several symplectic capacities, including the Ekeland–Hofer–Zehnder capacity, the displacement energy capacity, and the cylindrical capacity, are all equivalent up to a universal constant.
Cite this article
Efim D. Gluskin, Yaron Ostrover, Asymptotic equivalence of symplectic capacities. Comment. Math. Helv. 91 (2016), no. 1, pp. 131–144
DOI 10.4171/CMH/380