Pluripotential estimates on compact Hermitian manifolds
Slawomir Dinew, Slawomir Kolodziej
TL;DR
This paper studies complex Monge-Ampère equations on compact Hermitian manifolds, establishing uniform bounds and existence results for weak solutions, advancing pluripotential theory in this geometric setting.
Contribution
It provides $L^{ abla}$ estimates for Monge-Ampère equations on Hermitian manifolds and proves the existence of weak solutions under additional conditions.
Findings
Established $L^{ abla}$ bounds for solutions.
Proved existence of weak solutions under extra assumptions.
Extended pluripotential theory to Hermitian manifolds.
Abstract
We discuss pluripotential aspects of the Monge-Amp\`ere equations on compact Hermitian manifolds and prove estimates for any metric, as well as the existence of weak solutions under an extra assumption.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory