Cohn--Vossen-Type Inequalities for Three-Manifolds and Locally Conformally Flat Manifolds

We prove Cohn--Vossen-type scalar curvature inequalities on complete noncompact Riemannian manifolds with nonnegative Ricci curvature, motivated by Yau's higher-dimensional problem. For $n\ge3$, we obtain an $O(r^{n-2})$ normalized growth estimate under a $\mathbb Z^{n-2}$ subgroup condition on $π_1