Viterbo's weak systolic conjecture for convex contact forms

Let $b1$ be a convex contact form on $S^{2n-1}$. Its systolic ratio is defined by

$$\operatorname{sys}(S^{2n-1},\alpha)=\frac{\operatorname{min}\mleft\{{\{}\mright\}\text{period }T\text{ of an orbit}\}^n}{\operatorname{vol}(S^{2n-1},\alpha)},$$

where

$$\operatorname{vol}(S^{2n-1},\alpha)=\int_{S^{2n-1}}\alpha\wedge d\alpha^{n-1}.$$

Viterbo's weak conjecture. The systolic ratio satisfies

$$\operatorname{sys}(S^{2n-1},\alpha)\leq 1.$$

This conjecture is a systolic inequality for Reeb flows on convex contact boundaries. It is the weak Viterbo conjecture originally proposed by Viterbo; the supplied source does not indicate whether it has been resolved.