Relative volume comparison of Ricci Flow and its applications
Gang Tian, Zhenlei Zhang
TL;DR
This paper develops a new volume comparison estimate for Ricci flow, extending Perelman's no local collapsing estimate, and applies it to analyze the convergence of Kähler-Ricci flow on minimal manifolds.
Contribution
It introduces a generalized volume comparison estimate for Ricci flow, analogous to Bishop-Gromov, and demonstrates its application to Kähler-Ricci flow convergence.
Findings
Derived a relative volume comparison estimate for Ricci flow
Extended Perelman's no local collapsing estimate
Applied the estimate to Gromov-Hausdorff convergence of Kähler-Ricci flow
Abstract
In this paper, we derive a relative volume comparison estimate along Ricci flow and apply it to studying the Gromov-Hausdorff convergence of K\"ahler-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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research