Fake spherical spaceforms of constant positive scalar curvature.
Finiteness of and geometric inequalities in almost positive Ricci curvature
Finiteness theorems with integral conditions on curvature
Functional inequalities and manifolds with nonnegative weighted Ricci curvature
We show that -dimensional complete and noncompact metric measure spaces with nonnegative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are isometric to the model metric measure -space (i.e. the Euclidean metric -space). We also show that the Euclidean metric spaces are the only complete and noncompact metric measure spaces of nonnegative weighted Ricci curvature satisfying some prescribed Sobolev type inequality.