The local entropy along Ricci flow---Part B: the pseudo-locality theorems

Abstract

We localize the entropy functionals of G. Perelman and generalize his no-local-collapsing theorem and pseudo-locality theorem. Our generalization is technically inspired by further development of Li-Yau estimates along the Ricci flow. It has various applications, including to show the continuous dependence of the Ricci flow with respect to the initial metric in Gromov-Hausdorff topology with Ricci curvature bounded below, and to show the compactness of the moduli of Kähler manifolds with bounded scalar curvature and a rough locally almost Euclidean condition.

108 pages, 5 figures, comments welcome

References in corpus (1)

• Pointwise lower scalar curvature bounds for $C^0$ metrics via regularizing Ricci flow

Cited by in corpus (3)

• $d_p$ convergence and $\epsilon$-regularity theorems for entropy and scalar curvature lower bounds
• Small curvature concentration and Ricci flow smoothing
• Canonical diffeomorphisms of manifolds near spheres