Characterizing the range of the complex Monge-Amp\`ere operator
Songchen Liu
TL;DR
This paper extends the understanding of the complex Monge-Ampère operator by solving the equation for measures with pluripolar parts on compact Kähler manifolds, generalizing classical results.
Contribution
It introduces solutions for the complex Monge-Ampère equation with measures containing pluripolar parts on compact Kähler manifolds, broadening previous bounded domain results.
Findings
Solved the complex Monge-Ampère equation for measures with pluripolar parts
Generalized classical results from hyperconvex domains to compact Kähler manifolds
Discussed properties of the Monge-Ampère operator in special cases
Abstract
In this note, we solve the complex Monge-Amp\`ere equation for measures with a pluripolar part in compact K\"ahler manifolds. This result generalizes the classical results obtained by Cegrell in bounded hyperconvex domains. We also discuss the properties of the complex Monge-Amp\`ere operator in some special cases.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory