A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

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.2010 Mathematics Subject Classification. 53C55, 35J60, 32W20, 58J05.

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