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

DOI10.1515/crelle-2017-0017zbMath1435.32052arXiv1310.6326OpenAlexW3101732687MaRDI QIDQ2331058

Valentino Tosatti, Ben Weinkove

Publication date: 24 October 2019

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.6326

zbMATH Keywords

Monge-Ampère equationHermitian metricsGauduchon metricsGauduchon's conjecture

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Elliptic equations on manifolds, general theory (58J05) Kähler manifolds (32Q15) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05)

Related Items (31)

Curvature estimates for a class of Hessian type equations ⋮ Pogorelov type estimates for a class of Hessian quotient equations in Lorentz-Minkowski space \(\mathbb{R}_1^{n + 1} \) ⋮ On a class of Hessian type equations on Riemannian manifolds ⋮ The eigenvalue problem for Hessian type operator ⋮ Fully non-linear elliptic equations on compact manifolds with a flat hyperkähler metric ⋮ Pogorelov type estimates for a class of Hessian quotient equations ⋮ The Dirichlet problem for a class of prescribed curvature equations ⋮ The continuity equation of the Gauduchon metrics ⋮ Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds ⋮ Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds ⋮ On a class of Hessian quotient type equations on Riemannian manifolds ⋮ The Neumann Problem for a Class of Fully Nonlinear Elliptic Partial Differential Equations ⋮ A class of prescribed Weingarten curvature equations for locally convex hypersurfaces with boundary in \(\mathbb{R}^{n+1}\) ⋮ The weak solutions to complex Hessian equations ⋮ Fully non-linear elliptic equations on compact almost Hermitian manifolds ⋮ Curvature estimates for \(p\)-convex hypersurfaces of prescribed curvature ⋮ On the Alesker-Verbitsky conjecture on hyperKähler manifolds ⋮ Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms ⋮ Ricci curvatures on Hermitian manifolds ⋮ Second order estimates for complex Hessian equations with gradient terms on both sides ⋮ The continuity equation of almost Hermitian metrics ⋮ Fully non-linear degenerate elliptic equations in complex geometry ⋮ The parabolic Monge-Ampère equation on compact almost Hermitian manifolds ⋮ Scalar curvature on compact complex manifolds ⋮ On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones ⋮ Second order estimates for a class of complex Hessian equations on Hermitian manifolds ⋮ The Dirichlet problem on almost Hermitian manifolds ⋮ A flow of conformally balanced metrics with Kähler fixed points ⋮ Regularity of degenerate \(k\)-Hessian equations on closed Hermitian manifolds ⋮ Transverse fully nonlinear equations on Sasakian manifolds and applications ⋮ A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Kähler rank of compact complex manifolds
• On a uniform estimate for the quaternionic Calabi problem
• Geometric plurisubharmonicity and convexity: an introduction
• Form-type equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
• Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
• Weak transcendental holomorphic Morse inequalities on compact Kähler manifolds
• On the existence of special metrics in complex geometry
• A note on the cone of mobile curves
• La 1-forme de torsion d'une variété hermitienne compacte
• A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry
• The space of Kähler metrics.
• On projectively flat Hermitian manifolds
• On the evolution of a Hermitian metric by its Chern-Ricci form
• A second order estimate for complex Hess equations on a compact Kähler manifold
• Form-type Calabi-Yau equations
• Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics
• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
• The existence of supersymmetric string theory with torsion
• Relations between the Kähler cone and the balanced cone of a Kähler manifold
• Complex Monge-Ampère equations and totally real submanifolds
• On compact astheno-Kähler manifolds
• Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds
• Plurisubharmonic functions and nef classes on complex manifolds
• The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold
• Liouville and Calabi-Yau type theorems for complex Hessian equations
• The Calabi–Yau Theorem
• The complex Monge-Ampère equation on compact Hermitian manifolds
• Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
• Elliptic Partial Differential Equations of Second Order
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• On astheno-Kähler metrics
• Astheno-Kähler structures on Calabi–Eckmann manifolds

This page was built for publication: Hermitian metrics, \((n-1,n-1)\) forms and Monge-Ampère equations