Kähler-Ricci flow, Kähler-Einstein metric, and K-stability
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چکیده
We prove the existence of Kähler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kähler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kähler-Ricci flow on Fano manifolds. This is in turn based on a general finite dimensional discussion, which is interesting in its own and could potentially apply to other problems. As one application, we relate the asymptotics of the Calabi flow on a polarized Kähler manifold to K-stability assuming bounds on geometry.
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تاریخ انتشار 2015