The conformal symplectic Weinstein conjecture for rational exact lcs structures

Let $M$ be a closed manifold of dimension at least $4$, and let $(\lambda,\alpha)$ be an exact locally conformally symplectic structure, with $\alpha$ a rational Lee form. Define the vanishing distribution

$$\mathcal{V}_{\lambda}(p)=\{v\in T_pM\mid d\lambda(v,\cdot)=0\}$$

and the cone $C_{\lambda}\subset\mathcal{V}_{\lambda}$ by

$$C_{\lambda}(p)=\{v\in\mathcal{V}_{\lambda}(p)\mid\lambda(v)>0\}.$$

A Reeb curve is a smooth map $o:S^1\to M$ satisfying $\dot o(t)\in C_{\lambda}(o(t))$ for every $t$. Conformal symplectic Weinstein conjecture. There is a Reeb curve for $(M,\lambda,\alpha)$. This is presented as the basic conformal symplectic analogue of the Weinstein conjecture; the source does not state a resolution.