The Continuity Equation of the Gauduchon Metrics

Abstract

We study the continuity equation of the Gauduchon metrics and establish its interval of maximal existence, which extends the continuity equation of the K\"ahler metrics introduced by La Nave \& Tian for and of the Hermitian metrics introduced by Sherman \& Weinkove. Our method is based on the solution to the Gauduchon conjecture by Sz\'ekelyhidi, Tosatti \& Weinkove.