A class of fully nonlinear equations
Xiuxiong Chen, Weiyong He
TL;DR
This paper studies a broad class of fully nonlinear equations, including those by Donaldson and Gursky-Streets, providing solutions with uniform weak $C^2$ estimates even in degenerate cases.
Contribution
It introduces a unified approach to solving a class of fully nonlinear equations with new uniform weak $C^2$ estimates applicable to degenerate cases.
Findings
Established solutions with uniform weak $C^2$ estimates
Extended solvability to degenerate cases
Unified treatment of equations by Donaldson and Gursky-Streets
Abstract
In this paper we consider a class of fully nonlinear equations which cover the equation introduced by S. Donaldson a decade ago and the equation introduced by Gursky-Streets recently. We solve the equation with uniform weak estimates, which hold for degenerate case.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Mathematical Physics Problems