Estimates for complex singular Monge-Amp\`ere equations via integral method
Yunqing Wu, Kai Zheng
TL;DR
This paper develops new gradient and Laplacian estimates for solutions to singular complex Monge-Ampère equations using an integral method, advancing understanding of these complex geometric PDEs.
Contribution
It introduces an integral method approach to derive estimates for singular complex Monge-Ampère equations, which is a novel technique in this context.
Findings
Established gradient estimates for solutions.
Derived Laplacian estimates for solutions.
Applied the integral method to singular equations.
Abstract
In this paper, we obtain gradient estimates and Laplacian estimates for the solution to the singular complex Monge-Amp\`ere equation by applying the integral method.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics