2 problems

Let $(M^4,g)$ be a complete four-dimensional Riemannian manifold whose scalar curvature is bounded below by a positive constant and whose quotient satisfies $Q_g/R_g\geq k$ for som…

Let $(M^4,g)$ be a complete four-dimensional Riemannian manifold. Noncompact Bonnet–Myers conjecture. If … then $M^4$ is compact. This extends the corresponding proposition from co…