Interior estimates for solutions of Abreu's equation

Abstract

The paper develops various estimates for solutions of a fourth order nonlinear PDE, which corresponds to prescribing the scalar curvature of a toric Kahler metric.

Cited by in corpus (45)

• Extremal metrics on blow ups
• Space of Kähler metrics (IV)--On the lower bound of the K-energy
• Extremal metrics and K-stability (PhD thesis)
• Affine techniques on extremal metrics on toric surfaces
• Space of Kähler metrics III--On the lower bound of the Calabi energy and geodesic distance
• Deformations from a given Kähler metric to a twisted cscK metric
• Singular Abreu equations and minimizers of convex functionals with a convexity constraint
• Extremal Kähler metrics on projective bundles over a curve
• The global existence and convergence of the Calabi flow on ${\mathbb{C}}^n/{\mathbb{Z}}^n+i{\mathbb{Z}}^n$
• Geometric properties of boundary sections of solutions to the Monge--Ampère equation and applications
• The Calabi flow on toric Fano surface
• Extremal metrics on toric surfaces
• The Kahler Metrics of constant scalar curvature on the Complex Torus
• Pseudo-Calabi Flow
• Convergence of the calabi flow on toric varieties and related Kaehler manifolds
• Resolution a la Kronheimer of ${\mathbb{C}}^3/\Gamma$ singularities and the Monge-Ampere equation for Ricci-flat Kaehler metrics in view of D3-brane solutions of supergravity
• Boundary regularity for solutions to the linearized Monge-Ampère equations
• Modified Futaki invariant and equivariant Riemann-Roch formula
• Kähler non-collapsing, eigenvalues and the Calabi flow
• Bernstein Problem of Affine Maximal Type Hypersurfaces on Dimension N>=3
• Ambikaehler geometry, ambitoric surfaces and Einstein 4-orbifolds
• Prescribed Scaler Curvatures for Homogeneous Toric Bundles
• Some minimization problems in the class of convex functions with prescribed determinant
• Interior regularity on the Abreu equation
• $W^{4,p}$ solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations
• Monge Ampère functionals and the second boundary value problem
• Interior estimates for Monge-Ampère type fourth order equations
• The interior regularity of the Calabi flow on a toric surface
• Differential inequalities on homogeneous toric bundles
• An obstacle problem for a class of Monge-Ampère type functionals
• A uniform version of the Yau-Tian-Donaldson correspondence for extremal Kähler metrics on polarized toric manifolds
• Some Estimates for a Generalized Abreu's Equation
• Interior Regularity for a generalized Abreu Equation
• Interior Estimates for the $n$-dimensional Abreu's Equation
• The complex Monge-Ampere equation on compact Kaehler manifolds
• Calabi flow on projective bundles, I
• The second boundary value problem of the prescribed affine mean curvature equation and related linearized Monge-Ampère equation
• Solvability of a class of singular fourth order equations of Monge-Ampère type
• Scalar Curvature and Stability of Toric Fibrations
• Finiteness of $\mathbb{Q}$-Fano compactifications of semisimple group with Kähler-Einstein metrics
• $G$-Sasaki manifolds and K-energy
• Periodic solutions of Abreu's equation
• On the extension and smoothing of the Calabi flow on complex tori
• Interior second derivative estimates for solutions to the linearized Monge--Ampère equation
• The first boundary value problem for Abreu's equation