On the finite time collapsing rate of Kähler-Ricci flow on projective bundles

Abstract

This paper is concerned with a class of finite time collapsing rate along Kähler-Ricci flow on projective bundles. It is shown that the diameter of the fibers tend to zero at the rate ( T − t ) 1 2 − ϵ (T-t)^{\frac {1}{2}-\epsilon } for any ϵ > 0 \epsilon >0 as t t approaches the singular time T . T.