Vol. 305, No. 2, 2020

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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 2 with the standard symplectic structure we consider the bidisc D2 × D2 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 D2 × D2 . 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
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