Affine techniques on extremal metrics on toric surfaces

Abstract

This paper consists of real and complex affine techniques for studying the Abreu equation on toric surfaces. In particular, an interior estimate for Ricci tensor is given.

References in corpus (7)

• Interior estimates for solutions of Abreu's equation
• Extremal metrics on blow ups
• Extremal metrics and K-stability (PhD thesis)
• The Calabi flow on Kähler surface with bounded Sobolev constant
• The Kahler Metrics of constant scalar curvature on the Complex Torus
• Interior regularity on the Abreu equation
• Complete Affine K$\ddot{a}$hler Manifolds

Cited by in corpus (9)

• Extremal metrics on toric surfaces
• Uniform K-stability for extremal metrics on toric varieties
• A Liouville Theorem on the PDE $\det (f_{i\bar{j}})=1$
• Prescribed Scaler Curvatures for Homogeneous Toric Bundles
• Complete Affine K$\ddot{a}$hler Manifolds
• Differential inequalities on homogeneous toric bundles
• Interior Estimates for the $n$-dimensional Abreu's Equation
• Interior Regularity for a generalized Abreu Equation
• Some Estimates for a Generalized Abreu's Equation