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arXiv · 1609.07854

A parabolic Monge-Ampère type equation of Gauduchon metrics

Tao Zheng
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Abstract

We prove the long time existence and uniqueness of solution to a parabolic Monge-Ampère type equation on compact Hermitian manifolds. We also show that the normalization of the solution converges to a smooth function in the smooth topology as $t$ approaches infinity which, up to scaling, is the solution to a Monge-Ampère type equation. This gives a parabolic proof of the Gauduchon conjecture based on the solution of Székelyhidi, Tosatti and Weinkove to this conjecture.

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Tao Zheng. 2017-11-02. A parabolic Monge-Ampère type equation of Gauduchon metrics. https://doi.org/10.1093/imrn%2Frnx285

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