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The Journal of Geometric Analysis

, Volume 25, Issue 2, pp 1098–1107 | Cite as

On the Collapsing Rate of the Kähler–Ricci Flow with Finite-Time Singularity

  • Frederick Tsz-Ho FongEmail author
Article

Abstract

We study the collapsing behavior of the Kähler–Ricci flow on a compact Kähler manifold X admitting a holomorphic submersion \(X \xrightarrow{\pi} \varSigma\), where Σ is a Kähler manifold with \(\dim_{\mathbb{C}}\varSigma< \dim_{\mathbb{C}}X\). We give cohomological and curvature conditions under which the fibers π −1(z), zΣ collapse at the optimal rate \(\operatorname{diam}_{t} (\pi^{-1}(z)) \sim(T-t)^{1/2}\).

Keywords

Ricci flow Kähler Fibration 

Mathematics Subject Classification (2010)

Primary 53C44 

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Copyright information

© Mathematica Josephina, Inc. 2013

Authors and Affiliations

  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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