Interior estimates for solutions of Abreu equation

zbMath1085.53063arXivmath/0407486MaRDI QIDQ2567327

Simon K. Donaldson

Publication date: 30 September 2005

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407486

zbMATH Keywords

toric varietiesMonge-Ampère equationKähler geometryAbreu's equationa priori estimation of solutions

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Nonlinear higher-order PDEs (35G20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (59)

Solvability of a class of singular fourth order equations of Monge-Ampère type ⋮ The HcscK equations in symplectic coordinates ⋮ Extremal metrics on toric surfaces ⋮ Variational solutions to extremal metrics on toric surfaces ⋮ \(W^{4, p}\) solution to the second boundary value problem of the prescribed affine mean curvature and Abreu's equations ⋮ Generalized Kähler-Ricci flow on toric Fano varieties ⋮ On the extension and smoothing of the Calabi flow on complex tori ⋮ Extremal Kähler Poincaré type metrics on toric varieties ⋮ \(G\)-Sasaki manifolds and K-energy ⋮ Differential inequalities on homogeneous toric bundles ⋮ Global \(W^{1,p}\) estimates for solutions to the linearized Monge-Ampère equations ⋮ Prescribed scalar curvatures for homogeneous toric bundles ⋮ Numerical Approximations to Extremal Toric Kähler Metrics with Arbitrary Kähler Class ⋮ Extremal metrics on toric manifolds and homogeneous toric bundles ⋮ Regularity of Hamiltonian stationary equations in symplectic manifolds ⋮ Interior estimates for the Monge-Ampère type fourth order equations ⋮ Bernstein problem of affine maximal type hypersurfaces on dimension \(N \geq 3\) ⋮ Remarks on sharp boundary estimates for singular and degenerate Monge-Ampère equations ⋮ The Abreu equation with degenerated boundary conditions ⋮ The Guillemin boundary problem for Monge-Ampère equation in the polygon ⋮ A Note on Extremal Toric Almost Kähler Metrics ⋮ Interior regularity on the Abreu equation ⋮ Modified Futaki invariant and equivariant Riemann-Roch formula ⋮ Singular Kähler-Einstein metrics on \(\mathbb{Q}\)-Fano compactifications of Lie groups ⋮ Boundary regularity for solutions to the linearized Monge-Ampère equations ⋮ The global existence and convergence of the Calabi flow on \(\mathbb C^{n}/\mathbb Z^{n}+i \mathbb Z^{n}\) ⋮ Interior gradient estimates for solutions to the linearized Monge-Ampère equation ⋮ Toric aspects of the first eigenvalue ⋮ A Bernstein theorem for affine maximal-type hypersurfaces ⋮ Interior estimates for the \(n\)-dimensional Abreu's equation ⋮ Global \(W^{2,p}\) estimates for solutions to the linearized Monge-Ampère equations ⋮ Minimizing weak solutions for Calabi's extremal metrics on toric manifolds ⋮ The stability inequality for Ricci-flat cones ⋮ Deformations of extremal toric manifolds ⋮ Uniform K-stability for extremal metrics on toric varieties ⋮ Toric surfaces, \(K\)-stability and Calabi flow ⋮ The Bernstein theorem for a class of fourth order equations ⋮ Kähler–Einstein Metrics on Toric Manifolds and G-manifolds ⋮ Hamiltonian 2-forms in Kähler geometry. III: Extremal metrics and stability ⋮ The Monge-Ampère equation with Guillemin boundary conditions ⋮ The interior regularity of the Calabi flow on a toric surface ⋮ Notes on Chern's affine Bernstein conjecture ⋮ Extremal metrics on blowups ⋮ The complex Monge-Ampère equation on compact Kähler manifolds ⋮ On the extension of Calabi flow on toric varieties ⋮ Extremal Kähler metrics on projective bundles over a curve ⋮ A Bernstein property of a class of fourth order complex partial differential equations ⋮ A Bernstein theorem for affine maximal type hypersurfaces under decaying convexity ⋮ The Bernstein problem for affine maximal type hypersurfaces under decaying convexity ⋮ Space of Kähler metrics. III: On the lower bound of the Calabi energy and geodesic distance ⋮ Some estimates for the generalized Abreu equation ⋮ Resolution à la Kronheimer of \(\mathbb{C}^3/\Gamma\) singularities and the Monge-Ampère equation for Ricci-flat Kähler metrics in view of D3-brane solutions of supergravity ⋮ Global Hölder estimates for 2D linearized Monge-Ampère equations with right-hand side in divergence form ⋮ Interior regularity for the generalized Abreu equation ⋮ Interior second derivative estimates for solutions to the linearized Monge-Ampère equation ⋮ Convergence of the Calabi flow on toric varieties and related Kähler manifolds ⋮ Boundary Harnack inequality for the linearized Monge-Ampère equations and applications ⋮ A regularity theorem of the Abreu equation ⋮ 2-dimensional Kähler-Einstein metrics induced by finite dimensional complex projective spaces

This page was built for publication: Interior estimates for solutions of Abreu equation