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

Frederick Tsz-Ho Fong

Published 2011-12-27Version 1

This short note studies the collapsing behavior of the K\"ahler-Ricci flow on a compact K\"ahler manifold X admitting a holomorphic submersion X -> B where B is a K\"ahler 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}