Gauduchon metrics with prescribed volume form

Ben Weinkove; G\'abor Sz\'ekelyhidi; Valentino Tosatti

arxiv: 1503.04491 · v2 · pith:YAL5SYAZnew · submitted 2015-03-16 · 🧮 math.DG · math.AP· math.CV

Gauduchon metrics with prescribed volume form

G\'abor Sz\'ekelyhidi , Valentino Tosatti , Ben Weinkove This is my paper

classification 🧮 math.DG math.APmath.CV

keywords gauduchonmetricsformprescribedvolumechern-riccicompactcomplex

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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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Gauduchon metrics with prescribed volume form

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