Some curvature pinching results for Riemannian manifolds with density

William Wylie

Abstract: In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifold with density. In the Ricci curvature case the main result implies a diameter estimate that is new even for compact shrinking Ricci solitons. In the case of sectional curvature we prove a new sphere theorem.

Journal: Proc. Amer. Math. Soc.

DOI: 10.1090/proc/12853