Acta Mathematica

Volume 219 (2017)

Number 1

Gauduchon metrics with prescribed volume form

Pages: 181 – 211

DOI: https://dx.doi.org/10.4310/ACTA.2017.v219.n1.a6

Authors

Gábor Székelyhidi (Department of Mathematics, University of Notre Dame, Indiana, U.S.A.)

Valentino Tosatti (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

Ben Weinkove (Department of Mathematics, Northwestern University, Evanston, Illinois, U.S.A.)

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.

Full Text (PDF format)

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.

Received 12 October 2015

Accepted 6 December 2017

Published 31 January 2018