Gauduchon metrics with prescribed volume form
Differential Geometry
2018-02-02 v2 Analysis of PDEs
Complex Variables
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.
Cite
@article{arxiv.1503.04491,
title = {Gauduchon metrics with prescribed volume form},
author = {Gábor Székelyhidi and Valentino Tosatti and Ben Weinkove},
journal= {arXiv preprint arXiv:1503.04491},
year = {2018}
}
Comments
29 pages. Final version to appear in Acta Math