Solutions to weighted complex m-Hessian Equations on domains in Cn
Nguyen Van Phu, Nguyen Quang Dieu
TL;DR
This paper develops comparison principles for a specific operator to solve weighted complex m-Hessian equations in complex domains, advancing the understanding of these nonlinear PDEs.
Contribution
It introduces new comparison principles for the operator $H_{\chi,m}$, enabling solutions to weighted complex m-Hessian equations.
Findings
Established comparison principle for $H_{\chi,m}$
Solved certain weighted complex m-Hessian equations
Enhanced methods for nonlinear PDEs in complex analysis
Abstract
In this paper, we first study the comparison principle for the operator . This result is used to solve certain weighted complex Hessian equations.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations