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.

arXiv comment63 pages, 10 figures, comments welcome!

References in corpus (6)

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• Space of Ricci flows (II)
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• Riemannian geometry of Kahler-Einstein currents
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Cited by in corpus (6)

• Relative volume comparison of Ricci Flow and its applications
• 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
• Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
• Notes on Ricci flows with collapsing initial data (I): Distance distortion
• On a twisted conical Kähler-Ricci flow