Choquet-Monge-Ampere Classes
Vincent Guedj, Sibel Sahin, Ahmed Zeriahi
TL;DR
This paper introduces Choquet-Monge-Ampere classes on compact Kahler manifolds, analyzing their properties and comparing them with finite energy classes relevant in Kahler Geometry.
Contribution
It defines and studies a new class of quasi-plurisubharmonic functions based on Monge-Ampere capacity, expanding the understanding of function spaces in Kahler Geometry.
Findings
Choquet-Monge-Ampere classes are characterized by sublevel set capacity conditions.
Comparison established between Choquet-Monge-Ampere classes and finite energy classes.
Results enhance the understanding of function spaces in Kahler Geometry.
Abstract
We introduce and study Choquet-Monge-Ampere classes on compact Kahler manifolds. They consist of quasi-plurisubharmonic functions whose sublevel sets have small enough asymptotic Monge-Ampere capacity. We compare them with finite energy classes, which have recently played an important role in Kahler Geometry.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory