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
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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.4171/CMH/380

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Asymptotic equivalence of symplectic capacities

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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