Volume growth of 3-manifolds with scalar curvature lower bounds

Abstract

We give a new proof of a recent result of Munteanu–Wang relating scalar curvature to volume growth on a 3 3 -manifold with non-negative Ricci curvature. Our proof relies on the theory of μ \mu -bubbles introduced by Gromov [Geom. Funct. Anal. 28 (2018), pp. 645–726] as well as the almost splitting theorem due to Cheeger–Colding [Ann. of Math. (2) 144 (1996), pp. 189–237].