Asymptotic equivalence of symplectic capacities

Efim D. Gluskin; Yaron Ostrover

doi:10.4171/CMH/380

Asymptotic equivalence of symplectic capacities

Efim D. Gluskin
, Yaron Ostrover

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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 language	English GB
Pages (from-to)	131-144
Number of pages	14
Journal	Commentarii Mathematici Helvetici
Volume	91
Issue number	1
DOIs	https://doi.org/10.4171/CMH/380
State	Published - 2016

Keywords

Asymptotic behaviour
Convex bodies
Symplectic capacities

ASJC Scopus subject areas

General Mathematics

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10.4171/CMH/380

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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.",

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N2 - 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.

AB - 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.

KW - Asymptotic behaviour

KW - Convex bodies

KW - Symplectic capacities

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DO - 10.4171/CMH/380

M3 - مقالة

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Asymptotic equivalence of symplectic capacities

Abstract

Keywords

ASJC Scopus subject areas

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