The Kähler-Ricci flow and K-polystability

  title={The K{\"a}hler-Ricci flow and K-polystability},
  author={G{\'a}bor Sz{\'e}kelyhidi},
  • Gábor Székelyhidi
  • Published 2009
We consider the Kähler-Ricci flow on a Fano manifold. We show that if the curvature remains uniformly bounded along the flow, the Mabuchi energy is bounded below, and the manifold is K-polystable, then the manifold admits a Kähler-Einstein metric. The main ingredient is a result that says that a sufficiently small perturbation of a cscK manifold admits a cscK metric if it is K-polystable. 

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