The strong Viterbo conjecture for convex domains

Let $X\subset\mathbb{R}^{2n}$ be a convex domain. A symplectic capacity is normalized if it takes the same value on the unit ball and the unit symplectic cylinder. The strong Viterbo conjecture. All normalized symplectic capacities of $X$ should agree. This conjecture is stronger than the volume-capacity inequality and is also disproved in general: a counterexample to Viterbo's conjecture yields a convex domain for which the normalized capacities do not all agree.