Kähler-Ricci flow on a toric manifold with positive first Chern class

Abstract

In this note, we prove that on an $n$-dimensional compact toric manifold with positive first Chern class, the Kähler-Ricci flow with any initial $(S^1{)}^n$-invariant Kähler metric converges to a Kähler-Ricci soliton. In particular, we give another proof for the existence of Kähler-Ricci solitons on a compact toric manifold with positive first Chern class by using the Kähler-Ricci flow.

Cited by in corpus (1)

• Multiplier ideal sheaves and the Kähler-Ricci flow on toric Fano manifolds with large symmetry