On the Ekeland–Hofer symplectic capacities of the real bidisc

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.

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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

Vol. 305, No. 2, 2020

Luca Baracco, Martino Fassina and Stefano Pinton

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors