A new gradient estimate for the complex Monge-Amp\`ere equation
Bin Guo, Duong H. Phong, Freid Tong
TL;DR
This paper introduces an improved gradient estimate for complex Monge-Ampère equations, utilizing the ABP maximum principle to enhance existing bounds in certain aspects.
Contribution
It presents a novel gradient estimate for complex Monge-Ampère equations that advances previous results by applying the ABP maximum principle.
Findings
Enhanced gradient bounds for complex Monge-Ampère equations
Application of ABP maximum principle to complex PDEs
Improved estimates in specific cases
Abstract
A gradient estimate for complex Monge-Amp\`ere equations which improves in some respects on known estimates is proved using the ABP maximum principle.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons