Li's compactness conjecture for manifolds with uniformly convex boundary

Let $(M^n,g)$ be a complete Riemannian manifold with smooth nonempty boundary $\partial M$. Suppose $M$ has nonnegative Ricci curvature and $\partial M$ is uniformly convex, meaning that the second fundamental form $h$ satisfies

$$h\ge k>0$$

for some constant $k$. Li's compactness conjecture. Then $M$ is compact and $\pi_1(M)$ is finite. The conjecture generalizes Hamilton's compactness result for uniformly pinched convex hypersurfaces in Euclidean space and is a Bonnet–Myers-type statement with strict positivity imposed on the boundary. It is confirmed by the paper.