The local entropy along Ricci flow---Part A: the no-local-collapsing 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 estimate along the Ricci flow. It can be used to show the Gromov-Hausdorff convergence of the Kähler Ricci flow on each minimal projective manifold of general type.

63 pages, 10 figures, comments welcome!

References in corpus (4)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• The Kahler-Ricci flow through singularities
• Riemannian geometry of Kahler-Einstein currents
• On the Kahler Ricci flow on projective manifolds of general type

Cited by in corpus (2)

• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow