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In this short note, we show that given a special Kähler–Einstein degeneration with bounded geometry, for any noncentral fiber, there exists a Kähler–Ricci flow which converges to the Kähler–Einstein metric of the central fiber. As an example, Tian's deformations [ 12 ] of the Mukai 3-fold admit Kähler–Ricci flows which converge to Donaldson's Kähler–Einstein metric [ 5 ] over the Mukai 3-fold.

On the Kähler–Ricci Flows Near the Mukai–Umemura 3-Fold