The elliptic closed Reeb-orbit conjecture for strictly convex hypersurfaces

Let $\Sigma^{2n-1}$ bound a strictly convex domain in $\mathbb{R}^{2n}$. Elliptic orbit conjecture. There exists at least one elliptic closed Reeb orbit on $\Sigma$. The source describes this as a long-standing stability conjecture for closed Reeb orbits on compact convex hypersurfaces; it remains open in general, despite results under additional assumptions.