On the Ekeland-Hofer symplectic capacities of the real bidisc

TL;DR

This paper computes explicit Ekeland-Hofer symplectic capacities for the real bidisc in complex two-space and explores their implications for symplectic rigidity phenomena.

Contribution

It provides the first explicit calculations of multiple Ekeland-Hofer capacities for the real bidisc, advancing understanding of symplectic invariants.

Findings

Explicit values for the first three Ekeland-Hofer capacities of the real bidisc.

Insights into symplectic rigidity related to these capacities.

Potential applications to symplectic embedding problems.

Abstract

In $\mathbb{C}^2$ 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.