Wang–Xia sharp lower-bound conjecture for the first fourth-order Steklov eigenvalue

Let $(M^n,g)$, $n\geq 2$, be a connected compact smooth Riemannian manifold with boundary. Assume that $\operatorname{Ric}_g\geq 0$ and that the principal curvatures of the boundary $\partial M$ are bounded below by a constant $c>0$. Let $\lambda_1=\lambda_1(\partial M)$ denote the first nonzero eigenvalue of the Laplacian of $\partial M$, and let $\xi_1$ denote the first nonzero eigenvalue of the fourth-order Steklov problem. Wang–Xia's conjecture. The eigenvalue $\xi_1$ satisfies

$$\xi_1\geq \frac{n+2}{n-1}c\lambda_1,$$

with equality only for the Euclidean ball of radius $1/c$. This is a proposed sharp lower bound for the first nonzero eigenvalue of the fourth-order Steklov problem; the supplied source gives no resolution status.