English

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.

Keywords

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

R2 v1 2026-06-22T08:53:34.339Z