Interior estimates for solutions of Abreu's equation

2004/07/28 by Simon Donaldson, S. K. Donaldson, Donaldson, S. K. · 15 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.math/0407486

arxiv created 2005/05/05 · arxiv updated 2009/12/01

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

• The complex Monge-Ampere equation on compact Kaehler manifolds
• The eigenvalue problem for the Monge-Amp `ere operator on general\n bounded convex domains
• The second boundary value problem of the prescribed affine mean\n curvature equation and related linearized Monge-Amp `ere equation
• W^{4, p} solution to the second boundary value problem of the\n prescribed affine mean curvature and Abreu's equations
• Boundary regularity for solutions to the linearized Monge-Amp `ere\n equations
• Extremal metrics and K-stability (PhD thesis)
• The first boundary value problem for Abreu's equation
• Toric geometry of generalized Kähler-Ricci solitons
• Interior second derivative estimates for solutions to the linearized\n Monge--Amp `ere equation
• G-Sasaki manifolds and K-energy
• The interior regularity of the Calabi flow on a toric surface
• Space of Kähler metrics (IV)--On the lower bound of the K-energy
• Extremal metrics on toric surfaces
• Periodic solutions of Abreu's equation
• Scalar Curvature and Stability of Toric Fibrations

Related

• O(n) invariant solutions of Abreu's equation
• The Kahler Metrics of constant scalar curvature on the Complex Torus
• Interior Estimates for the n-dimensional Abreu's Equation
• Interior regularity on the Abreu equation
• Extremal metrics on toric surfaces, I