On the Ekeland–Hofer symplectic capacities of the real bidisc

Luca Baracco, Martino Fassina and Stefano Pinton

Vol. 305 (2020), No. 2, 423–446

DOI: 10.2140/pjm.2020.305.423

Abstract

In ${ℂ}^2$ with the standard symplectic structure we consider the bidisc $D^2\times D^2$ constructed as the product of two open real discs of radius $1$. We compute explicit values for the first, second and third Ekeland–Hofer symplectic capacity of $D^2\times D^2$. We discuss some applications to questions of symplectic rigidity.

Keywords

symplectic capacities, Lagrangian bidisc

Mathematical Subject Classification 2010

Primary: 53D05

Secondary: 53D35

Milestones

Received: 7 February 2019

Revised: 15 October 2019

Accepted: 26 November 2019

Published: 29 April 2020