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Gauduchon metrics with prescribed volume form

Gábor Székelyhidi University of Notre Dame Valentino Tosatti Northwestern University Ben Weinkove Northwestern University

Differential Geometry mathscidoc:1911.43017

Acta Mathematica, 219, (1), 181 – 211, 2017
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.
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@inproceedings{gábor2017gauduchon,
  title={Gauduchon metrics with prescribed volume form},
  author={Gábor Székelyhidi, Valentino Tosatti, and Ben Weinkove},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126160941521597528},
  booktitle={Acta Mathematica},
  volume={219},
  number={1},
  pages={181 – 211},
  year={2017},
}
Gábor Székelyhidi, Valentino Tosatti, and Ben Weinkove. Gauduchon metrics with prescribed volume form. 2017. Vol. 219. In Acta Mathematica. pp.181 – 211. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191126160941521597528.
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