The continuity equation of the Gauduchon metrics

Tao Zheng

Vol. 310 (2021), No. 2, 487–510

DOI: 10.2140/pjm.2021.310.487

Abstract

We study the continuity equation of the Gauduchon metrics and establish its interval of maximal existence, which extends the continuity equation of the Kähler metrics introduced by La Nave and Tian for and of the Hermitian metrics introduced by Sherman and Weinkove. Our method is based on the solution to the Gauduchon conjecture by Székelyhidi, Tosatti and Weinkove.

Keywords

continuity equation, Gauduchon metric, maximal time existence, Chern–Ricci form

Mathematical Subject Classification

Primary: 35J60, 53C55, 58J05

Milestones

Received: 25 April 2020

Revised: 22 September 2020

Accepted: 9 December 2020

Published: 8 March 2021