Interior estimates for solutions of Abreu's equation
S. K. Donaldson
TL;DR
This paper derives interior estimates for solutions to Abreu's equation, a complex fourth order nonlinear PDE related to scalar curvature in toric Kähler geometry.
Contribution
It introduces new interior estimate techniques for solutions of Abreu's equation, advancing understanding of scalar curvature problems in toric Kähler metrics.
Findings
Established bounds for solutions within interior regions.
Improved regularity results for solutions.
Enhanced understanding of scalar curvature prescription.
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Meromorphic and Entire Functions