Abstract
We prove that on any compact complex manifold one can find Gauduchon metrics with prescribed volume form. This is equivalent to prescribing the Chern–Ricci curvature of the metrics, and thus solves a conjecture of Gauduchon from 1984.
Funding Statement
Supported in part by National Science Foundation grants DMS-1306298 and DMS-1350696 (G. Sz.), DMS-1308988 (V.T.) and DMS-1406164 (B.W.). The second-named author is supported in part by a Sloan Research Fellowship.
Citation
Gábor Székelyhidi. Valentino Tosatti. Ben Weinkove. "Gauduchon metrics with prescribed volume form." Acta Math. 219 (1) 181 - 211, September 2017. https://doi.org/10.4310/ACTA.2017.v219.n1.a6
