The lower-positive-curvature conjecture for Stein manifolds

Let $M$ be a Stein manifold of complex dimension at least two, and let $A^2(M)$ be its Bergman space. Assume that $A^2(M)$ is base-point free and separates holomorphic directions. The lower-positive-curvature conjecture. The Bergman metric of $M$ cannot have holomorphic sectional curvatures bounded from below by a positive constant. The source proposes this as a more general open conjecture; it is motivated by the preceding constant-curvature conjecture and is not proved in the paper.