Gauduchon metrics with prescribed volume form

By G'abor Sz'ekelyhidi, Valentino Tosatti, B. Weinkove. 2015

185 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1d79b38f8b3b712583368f38b74c65eecf2045e1

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Strominger connection and pluriclosed metrics (2019, background): “any authors, and they have applications in type II string theory and in 2-dimensional supersymmetric σ-models. We refer the readers to [29], [13], [17], [20], [9], [10], [11], [32], [27], [28], [26], [30], [31], [21], [22], [23], [12] and the references therein for more discussions on Strominger con”
The Monge–Ampère equation for non-integrable almost complex structures (2016, methodology): “ ∈ Mwith λ1(∇2ϕ(x0)) >0. However, Qis not smooth in general, since the eigenspace associated to λ1 may have dimension strictly larger than 1. We deal with this using a perturbation argument, as in [40, 41]. First we discuss the choice of coordinate system in a neighborhood of x0. Let V1 be a unit”
Fully non-linear parabolic equations on compact Hermitian manifolds (2017, background): “Other adaptations to C(2) estimates can be found in [51], [32], [34], [67].”
A second order estimate for general complex Hessian equations (2015, methodology): “In particular, as a crucial step in the continuity method, C2 estimates for complex Hessian type equations have been studied in various settings; see [Hou et al. 2010; Sun 2014; Székelyhidi 2015; Székelyhidi et al. 2015; Zhang 2015].”
On Bismut flat manifolds (2016, background): “lution to the Gauduchon Conjecture by Sz´ekelyhidi, Tosatti, and Weinkove. We refer the readers to [33], [9], [10], [11], [12], [13], [24], [37], [19], [16], [17], [18], [25], [26], [27], [35], [36], [34] and the references therein for some recent progress in this area. Given a Hermitian manifold (M”