scientific article; zbMATH DE number 7629504

MaRDI QIDQ5056640

Tristan C. Collins, Sebastien Picard

Publication date: 8 December 2022

Full work available at URL: https://arxiv.org/abs/1909.00447

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

blow-up argumentexistence of a subsolutionsecond order a priori estimate of the solution

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Complex Monge-Ampère operators (32W20)

Related Items

The complex Hessian equations with gradient terms on Hermitian manifolds ⋮ Continuous solutions to complex Hessian equations on Hermitian manifolds ⋮ On the Hessian-cscK equations ⋮ The Dirichlet problem for Monge-Ampère type equations on Hermitian manifolds ⋮ Second order estimates for a class of complex Hessian equations on Hermitian manifolds

Cites Work

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• A second order estimate for general complex Hessian equations
• Solutions to degenerate complex Hessian equations
• Regularity of the geodesic equation in the space of Sasakian metrics
• \(C^{2,\alpha}\) estimates for nonlinear elliptic equations in complex and almost complex geometry
• On a class of fully nonlinear elliptic equations on Hermitian manifolds
• Interior a priori estimates for solutions of fully nonlinear equations
• Estimates for the complex Monge-Ampère equation on Hermitian and balanced manifolds
• The Dirichlet problem for degenerate complex Monge-Ampère equations
• Dirichlet duality and the nonlinear Dirichlet problem on Riemannian manifolds
• A new capacity for plurisubharmonic functions
• Hypersurfaces of constant curvature in hyperbolic space II
• Differentiability properties of symmetric and isotropic functions
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• The Dirichlet problem for complex Monge-Ampère equations and regularity of the pluri-complex Green function
• Boundary-value problems on \(S^ n\) for surfaces of constant Gauss curvature
• On the Dirichlet problem for Hessian equations
• Elliptic partial differential equations of second order
• New curvature flows in complex geometry
• The anomaly flow and the Fu-Yau equation
• Fully non-linear elliptic equations on compact Hermitian manifolds
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• The extremal function associated to intrinsic norms.
• On the \(C^{2,\alpha}\)-regularity of the complex Monge-Ampère equation
• The Dirichlet problem for the Monge-Ampère equations in Hermitian metric
• \((1,1)\) forms with specified Lagrangian phase: \textit{a priori} estimates and algebraic obstructions
• Second-order estimates and regularity for fully nonlinear elliptic equations on Riemannian manifolds
• Fu-Yau Hessian equations
• Second order estimates for a class of complex Hessian equations on Hermitian manifolds
• Moment maps, nonlinear PDE and stability in mirror symmetry. I: Geodesics
• The Dirichlet problem on almost Hermitian manifolds
• Solutions to the Hull-Strominger system with torus symmetry
• A second order estimate for complex Hess equations on a compact Kähler manifold
• Regularity of degenerate Hessian equations
• Mixed Hessian inequalities and uniqueness in the class \(\mathcal {E}(X,\omega ,m)\)
• Concavity of the Lagrangian phase operator and applications
• Hessian equations on closed Hermitian manifolds
• The Fu-Yau equation with negative slope parameter
• The Fu-Yau equation in higher dimensions
• The Dirichlet problem for a complex Monge-Ampère type equation on Hermitian manifolds
• The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation
• A priori estimates for complex Hessian equations
• Weak solutions to the complex Hessian equation.
• Complex Monge-Ampère equations and totally real submanifolds
• Degenerate complex Hessian equations on compact Kahler manifolds
• Boundary Regularity for Viscosity Solutions of Fully Nonlinear Elliptic Equations
• Liouville and Calabi-Yau type theorems for complex Hessian equations
• A Priori Estimates for Complex Monge-Ampere Equation on Hermitian Manifolds
• Monge–Ampère Equations on Complex Manifolds with Boundary
• The complex Monge-Ampère equation on compact Hermitian manifolds
• An Eigenvalue for the Product of Normal Matrices
• Complex Hessian Equation on Kähler Manifold
• Nonlinear elliptic equations and the complex hessian
• Mixed volume forms and a complex equation of Monge-Ampère type on Kähler manifolds of positive curvature
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
• Classical solutions of fully nonlinear, convex, second-order elliptic equations
• On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• The dirichlet problem for a class of fully nonlinear elliptic equations
• The Dirichlet problem for a complex Hessian equation on compact Hermitian manifolds with boundary
• On a Class of Fully Nonlinear Elliptic Equations Containing Gradient Terms on Compact Hermitian Manifolds
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• Fully non-linear parabolic equations on compact Hermitian manifolds
• Weak solutions of complex Hessian equations on compact Hermitian manifolds
• Subsolution theorem for the complex Hessian equation
• Complex Monge Ampere Equations
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
• Complex Hessian equations on some compact Kähler manifolds