On the collapsing rate of the Kähler-Ricci flow with finite-time singularity

2011/12/27 by Fong, Frederick Tsz-Ho · 2 citations
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1112.5987

Abstract

This short note studies the collapsing behavior of the Kähler-Ricci flow on a compact Kähler manifold X admitting a holomorphic submersion X -> B where B is a Kähler manifold of lower dimension than X. We give cohomological and curvature conditions under which the fibers collapse at the optimal rate ~(T-t)^1/2

Cited by

• Fano Fibrations and Twisted Kähler-Einstein Metrics II: The Kähler-Ricci Flow
• Fano Fibrations and Twisted Kähler-Einstein Metrics I

Related

• Collapsing immortal Kähler-Ricci flows
• Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow
• Finite time singularities of the Kähler-Ricci flow
• Scalar Curvature Behavior for Finite Time Singularity of Kähler-Ricci Flow
• Global Ricci Curvature Behaviour for the Kähler-Ricci Flow with Finite Time Singularities