EHZ capacity versus cylindrical capacity on convex domains

Determine whether the Ekeland–Hofer–Zehnder capacity c_EHZ coincides with the cylindrical capacity c_Z on the class of convex domains in R^{2n}.

Background

For convex domains, there are three principal capacities considered: the Gromov width, the EHZ capacity, and the cylindrical capacity. The counterexample in the paper shows that the Gromov width differs from the EHZ capacity.

In R^{4}, the first embedded contact homology (ECH) capacity coincides with the cylindrical capacity for dynamically convex domains, but whether the EHZ capacity coincides with the cylindrical capacity for convex domains is unresolved. In the specific example K × T of rotated pentagons discussed in the paper, these two capacities coincide.