Akopyan–Karasev–Petrov conjecture on subadditivity of the Ekeland-Hofer-Zehnder capacity

Let $K,K_1,\ldots,K_m$ be convex bodies in $T^*\mathbb R^n$. Akopyan–Karasev–Petrov conjecture. If

$$K\subset\bigcup_{i=1}^m K_i,$$

then

$$c_{\mathrm{EHZ}}(K)\leq\sum_{i=1}^m c_{\mathrm{EHZ}}(K_i).$$

The conjecture is a subadditivity principle for the Ekeland-Hofer-Zehnder capacity under finite coverings by convex bodies. It is known for hyperplane cuts of round balls and, more generally, arbitrary convex bodies, but is open in the stated generality; convexity of the covering sets is essential.