A priori estimate for the complex Monge-Ampere equation
Wang Jiaxiang, Wang Xu-jia, Zhou Bin
TL;DR
This paper establishes a Moser-Trudinger type inequality for plurisubharmonic functions using a gradient flow approach to the complex Monge-Ampère functional, advancing theoretical understanding in complex analysis.
Contribution
It introduces a new inequality for plurisubharmonic functions and employs a gradient flow method for the complex Monge-Ampère equation, which is novel.
Findings
Proved a Moser-Trudinger type inequality for plurisubharmonic functions.
Developed a gradient flow technique for the complex Monge-Ampère functional.
Enhanced theoretical tools for complex analysis and PDEs.
Abstract
In this paper, we prove a Moser-Trudinger type inequality for pluri-subharmonic functions vanishing on the boundary. Our proof uses a descent gradient flow for the complex Monge-Ampere functional.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory