Local smoothing results for the Ricci flow in dimensions two and three

Abstract

We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality results of G.Perelman in dimension two.

20 pages. V.2 Fixed some typos in the statements of some of the theorems (some of the constants were written incorrectly). Fixed some typos realting to constants in section 3. Added a remark at the end of the paper which explains how Theorem 1.5 follows from Theorem 5.1. All proofs and the rest of the paper remain/remains unchanged

References in corpus (2)

• Notes on Perelman's papers
• Local curvature bound in Ricci flow

Cited by in corpus (3)

• Ricci de Turck flow on singular manifolds
• Stability of Ricci de Turck flow on Singular Spaces
• Bounded Ricci Curvature and Positive Scalar Curvature under Singular Ricci de Turck Flow