Effective volume growth of three-manifolds with positive scalar curvature

Abstract

In this note, we prove an effective linear volume growth for complete three-manifolds with non-negative Ricci curvature and uniformly positive scalar curvature. This recovers the results obtained by Munteanu-Wang. Our method builds upon recent work by Chodosh-Li-Stryker, which utilizes the technique of $\mu$-bubbles and the almost-splitting theorem by Cheeger-Colding.

arXiv comment10 pages; v2: minor changes, version accepted for publication in Proc. Amer. Math. Soc