Weak Solutions To Complex Monge-Amp\`ere Equation on hyperconvex domains
Slimane Benelkourchi
TL;DR
This paper proves a broad existence theorem for weak solutions to the complex Monge-Ampère equation within hyperconvex domains, advancing the understanding of complex analysis and PDEs in complex geometry.
Contribution
It introduces a general existence result for weak solutions to the complex Monge-Ampère equation on hyperconvex domains, expanding previous theoretical frameworks.
Findings
Established a general existence theorem for weak solutions
Applicable to a wide class of hyperconvex domains
Enhances the theoretical foundation of complex Monge-Ampère equations
Abstract
We show a very general existence theorem to the complex Monge-Amp\`ere type equation on hyperconvex domains.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations