On the K\"ahler-Ricci flows near the Mukai-Umemura 3-fold

Abstract

In this short note, we show that given a special K\"ahler-Einstein degeneration with bounded geometry, for any noncentral fiber, there exists a K\"ahler-Ricci flow which converges to the K\"ahler-Einstein metric of the central fiber. As an example, Tian's deformations \cite{Tian97} of the Mukai 3-fold admit K\"ahler-Ricci flows which converge to Donaldson's K\"ahler-Einstein metric \cite{Don08} over the Mukai 3-fold.