The complex Monge-Amp\`ere equation on compact Hermitian manifolds
Valentino Tosatti, Ben Weinkove
TL;DR
This paper proves that the complex Monge-Ampère equation on compact Hermitian manifolds always has a smooth solution, up to a scaling factor, extending known results in complex geometry.
Contribution
It establishes the existence of smooth solutions to the complex Monge-Ampère equation on compact Hermitian manifolds, a significant generalization of previous results on Kähler manifolds.
Findings
Existence of smooth solutions up to scaling
Extension of Monge-Ampère equation solutions to Hermitian manifolds
Advancement in complex differential geometry
Abstract
We show that, up to scaling, the complex Monge-Ampere equation on compact Hermitian manifolds always admits a smooth solution.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory