The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold
From MaRDI portal
Publication:2957314
DOI10.1090/jams/875zbMath1366.32015arXiv1305.7511OpenAlexW1517537245MaRDI QIDQ2957314
Ben Weinkove, Valentino Tosatti
Publication date: 26 January 2017
Published in: Journal of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1305.7511
Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Complex Monge-Ampère operators (32W20) Plurisubharmonic functions and generalizations (32U05)
Related Items (56)
Fully nonlinear elliptic equations on Hermitian manifolds for symmetric functions of partial Laplacians ⋮ 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 ⋮ Hessian equations on closed Hermitian manifolds ⋮ The Fu-Yau equation with negative slope parameter ⋮ The Neumann problem for a type of fully nonlinear complex equations ⋮ Aeppli Cohomology Classes Associated with Gauduchon Metrics on Compact Complex Manifolds ⋮ Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds ⋮ The Dirichlet problem for Monge-Ampère type equations on Hermitian manifolds ⋮ On a class of Hessian quotient type equations on Riemannian manifolds ⋮ Holomorphic deformations of balanced Calabi-Yau $\partial \bar{\partial}$-manifolds ⋮ Interior Hessian estimates for a class of Hessian type equations ⋮ Uniqueness of solutions to a class of mixed Hessian quotient type equations ⋮ On a Class of Fully Nonlinear Elliptic Equations on Closed Hermitian Manifolds II:L∞Estimate ⋮ Interior $C^{2}$ estimates for the Hessian quotient type equation ⋮ Monge-Ampère type equations on almost Hermitian 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 \(\mathbb{R}^{n+1}\) ⋮ 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 ⋮ \(m\)-subharmonic and \(m\)-plurisubharmonic functions: on two problems of Sadullaev ⋮ Hypersurfaces of prescribed mixed Weingarten curvature ⋮ Interior estimates for p-plurisubharmonic functions ⋮ Geometric flows and supersymmetry ⋮ Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds ⋮ Geometric flows and Strominger systems ⋮ Fully nonlinear elliptic equations for conformal deformations of Chern-Ricci forms ⋮ Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds ⋮ Stability and regularity of solutions of the Monge-Ampère equation on Hermitian manifolds ⋮ The Fu-Yau equation on compact astheno-Kähler manifolds ⋮ \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry ⋮ Fully non-linear degenerate elliptic equations in complex geometry ⋮ The parabolic Monge-Ampère equation on compact almost Hermitian manifolds ⋮ The Monge-Ampère equation for non-integrable almost complex structures ⋮ Minimal complex surfaces with Levi-Civita Ricci-flat metrics ⋮ Relations between the Kähler cone and the balanced cone of a Kähler manifold ⋮ Fu-Yau Hessian equations ⋮ The Dirichlet problem on almost Hermitian manifolds ⋮ Levi-Civita Ricci-flat metrics on compact complex manifolds ⋮ Hadamard-type inequalities for \(k\)-positive matrices ⋮ Regularity of degenerate Hessian equations ⋮ A flow of conformally balanced metrics with Kähler fixed points ⋮ Hermitian metrics, \((n-1,n-1)\) forms and Monge-Ampère equations ⋮ Transverse fully nonlinear equations on Sasakian manifolds and applications ⋮ A Parabolic Monge–Ampère Type Equation of Gauduchon Metrics ⋮ A spectral characterization and an approximation scheme for the Hessian eigenvalue ⋮ The \(L_p\) Minkowski type problem for a class of mixed Hessian quotient equations ⋮ Local regularity for concave homogeneous complex degenerate elliptic equations dominating the Monge-Ampère equation ⋮ \(C^{2,\alpha}\) regularities and estimates for nonlinear elliptic and parabolic equations in geometry
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Local Calabi and curvature estimates for the Chern-Ricci flow
- Convergence of the parabolic complex Monge-Ampère equation on compact Hermitian manifolds
- Balanced metrics on non-Kähler Calabi-Yau threefolds
- Geometric plurisubharmonicity and convexity: an introduction
- Hölder continuous solutions to complex Hessian equations
- Form-type equations on Kähler manifolds of nonnegative orthogonal bisectional curvature
- Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
- The Dirichlet problem for degenerate complex Monge-Ampère equations
- Geometry of compact complex homogeneous spaces with vanishing first Chern class
- Dirichlet duality and the nonlinear Dirichlet problem on Riemannian manifolds
- On the existence of special metrics in complex geometry
- A note on the cone of mobile curves
- A constant rank theorem for Hermitian \(k\)-convex solutions of complex Laplace equations
- P-convex Riemannian manifolds
- Deformation of Kähler metrics to Kähler-Einstein metrics on compact Kähler manifolds
- The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
- A local index theorem for non-Kähler manifolds
- The Dirichlet problem for a complex Monge-Ampère equation
- Properties of manifolds with skew-symmetric torsion and special holonomy
- On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
- Viscosity solutions to complex Hessian equations
- Hessian measures. II
- 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
- A priori estimates for complex Hessian equations
- Relations between the Kähler cone and the balanced cone of a Kähler manifold
- Collapsing of the Chern-Ricci flow on elliptic surfaces
- Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class
- Weak solutions to the complex Hessian equation.
- Complex Monge-Ampère equations and totally real submanifolds
- Cocalibrated G_2-manifolds with Ricci flat characteristic connection
- The Chern–Ricci flow on complex surfaces
- A Priori Estimates for Complex Monge-Ampere Equation on Hermitian Manifolds
- The complex Monge-Ampère equation on compact Hermitian manifolds
- Complex Hessian Equation on Kähler Manifold
- Mixed volume forms and a complex equation of Monge-Ampère type on Kähler manifolds of positive curvature
- 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
- A variational theory of the Hessian equation
- The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
- On Pointwise Gradient Estimates for the Complex Monge-Ampere Equation
- Existence, Uniqueness and Removable Singularities for Nonlinear Partial Differential Equations in Geometry
- Complex Monge Ampere Equations
- Complex Hessian equations on some compact Kähler manifolds
This page was built for publication: The Monge-Ampère equation for (𝑛-1)-plurisubharmonic functions on a compact Kähler manifold