Prefer a chat interface with context about you and your work?
Some curvature pinching results for Riemannian manifolds with density
In this note we consider versions of both Ricci and sectional curvature pinching for Riemannian manifolds 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 …