Relative volume comparison of Ricci Flow and its applications

Abstract

In this paper, we derive a relative volume comparison estimate along Ricci flow and apply it to studying the Gromov-Hausdorff convergence of Kähler-Ricci flow on a minimal manifold. This new estimate generalizes Perelman's no local collapsing estimate and can be regarded as an analogue of the Bishop-Gromov volume comparison for Ricci flow.

28 pages; minor change in the proof of Lemma 3.1

References in corpus (3)

• Riemannian geometry of Kahler-Einstein currents
• The local entropy along Ricci flow---Part A: the no-local-collapsing theorems
• The continuity method on minimal elliptic Kähler surfaces

Cited by in corpus (8)

• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Local curvature estimates of long-time solutions to the Kähler-Ricci flow
• A "boundedness implies convergence" principle and its applications to collapsing estimates in Kähler geometry
• Diameter and Ricci curvature estimates for long-time solutions of the Kahler-Ricci flow
• Infinite-time singularity type of the Kähler-Ricci flow
• Twisted Kähler-Einstein Metrics and Collapsing
• Notes on Ricci flows with collapsing initial data (I): Distance distortion
• The K"ahler-Ricci flow with Log Canonical Singularities