Kähler–Ricci flow, Kähler–Einstein metric, and K–stability

By Xiuxiong Chen, Song Sun, Bing Wang. Geometry and Topology, 2015

91 citations recorded by the source corpus.

We prove the existence of Kahler-Einstein metric on a K-stable Fano manifold using the recent compactness result on Kahler-Ricci flows. The key ingredient is an algebro-geometric description of the asymptotic behavior of Kahler-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 Kahler manifold to K-stability assuming bounds on geometry.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f32e1a12ab440ab515649e7b73143c6f32b31b0b

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The Kähler–Ricci flow and optimal degenerations (2016, methodology): “In fact such an optimal R-degeneration is given by the filtration constructed by Chen-Sun-Wang [9] using the Kähler-Ricci flow.”