Vol. 310, No. 2, 2021

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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
Authors
Tao Zheng
School of Mathematics and Statistics
Beijing Institute of Technology
Beijing
China