Existence and applications of Ricci flows via pseudolocality

Abstract

We prove the short-time existence of Ricci flows on complete manifolds with scalar curvature bounded below uniformly, Ricci curvature bounded below by a negative quadratic function, and with almost Euclidean isoperimetric inequality holds locally. In particular, this result applies to manifolds with both Ricci curvature and injectivity radius bounded from below. We also study the short-time behaviour of these solutions which may have unbounded curvature at the initial time, and provide some applications. A key tool is Perelman's pseudolocality theorem.

Final version. To appear in CAG Volume 32, No 7, 2024

References in corpus (5)

• Short-time existence of the Ricci flow on complete, non-collapsed $3$-manifolds with Ricci curvature bounded from below
• Strong Uniqueness of the Ricci Flow
• Deforming complete Hermitian metrics with unbounded curvature
• Kähler-Ricci flow with unbounded curvature
• Existence, Lifespan and Transfer Rate of Ricci Flows on Manifolds with Small Ricci Curvature

Cited by in corpus (6)

• Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II
• Chern-Ricci flows on noncompact complex manifolds
• On existence and curvature estimates of Ricci flow
• Small curvature concentration and Ricci flow smoothing
• A note on existence of exhaustion functions and its applications
• Some local Maximum principles along Ricci Flow