Hermitian metrics, (n-1,n-1) forms and Monge–Ampère equations

By Valentino Tosatti, B. Weinkove. Journal für die Reine und Angewandte Mathematik, 2013

102 citations recorded by the source corpus.

Abstract We show existence of unique smooth solutions to the Monge–Ampère equation for ( n - 1 ) (n-1) -plurisubharmonic functions on Hermitian manifolds, generalizing previous work of the authors. As a consequence we obtain Calabi–Yau theorems for Gauduchon and strongly Gauduchon metrics on a class of non-Kähler manifolds: those satisfying the Jost–Yau condition known as Astheno–Kähler. Gauduchon conjectured in 1984 that a Calabi–Yau theorem for Gauduchon metrics holds on all compact complex manifolds. We discuss another Monge–Ampère equation, recently introduced by Popovici, and show that the full Gauduchon conjecture can be reduced to a second-order estimate of Hou–Ma–Wu type.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aeeb1cd2c86d82f86bea599d68f23197d918b053

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In Applied Mathematics

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Citations in the corpus

Fully non-linear elliptic equations on compact Hermitian manifolds (2015, methodology): “s for more general types of equations, where the matrix Ain the equation F(A) = hdepends on the gradient of uas well. We illustrate this with an example taken from the recent work of Tosatti-Weinkove [31] on (n− 1)-plurisubharmonic functions. On a Hermitian manifold (M,α), given another Hermitian me”