#### Vol. 305, No. 2, 2020

 Recent Issues Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
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 ${D}^{2}×{D}^{2}$ 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 ${D}^{2}×{D}^{2}$. We discuss some applications to questions of symplectic rigidity.

##### Keywords
symplectic capacities, Lagrangian bidisc
Primary: 53D05
Secondary: 53D35
##### Milestones
Revised: 15 October 2019
Accepted: 26 November 2019
Published: 29 April 2020
##### Authors
 Luca Baracco Dipartimento di Matematica Tullio Levi-Civita Università degli studi di Padova Padova Italy Martino Fassina Department of Mathematics University of Illinois Urbana, IL United States Stefano Pinton Dipartimento di Matematica Politecnico di Milano Milano Italy