Asymptotic equivalence of symplectic capacities

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Abstract

A long-standing conjecture states that all normalized symplectic capacities coincide on the class of convex subsets of ℝ2n. 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 ℝ2n, 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.

Original languageEnglish
Pages (from-to)131-144
Number of pages14
JournalCommentarii Mathematici Helvetici
Volume91
Issue number1
DOIs
StatePublished - 2016

Funding

FundersFunder number
Horizon 2020 Framework Programme
European Research Council
Israel Science Foundation1274/14
Horizon 2020637386

    Keywords

    • Asymptotic behaviour
    • Convex bodies
    • Symplectic capacities

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