Hessian boundary measures

DOI10.1142/S0129167X19500162zbMath1416.32017OpenAlexW2918147142MaRDI QIDQ4631364

van Thien Nguyen

Publication date: 24 April 2019

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x19500162

zbMATH Keywords

capacityboundary measure\(m\)-subharmonic functioncomplex Hessian operator

Mathematics Subject Classification ID

Plurisubharmonic functions and generalizations (32U05) General pluripotential theory (32U15) Capacity theory and generalizations (32U20)

Cites Work

• Local property of a class of \(m\)-subharmonic functions
• Capacities and Hessians in the class of \(m\)-subharmonic functions
• Solutions to degenerate complex Hessian equations
• Hölder continuous solutions to complex Hessian equations
• Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
• Pluricomplex energy
• The geometry of \(m\)-hyperconvex domains
• On the Dirichlet problems for symmetric function equations of the eigenvalues of the complex Hessian
• The general definition of the complex Monge-Ampère operator.
• Viscosity solutions to complex Hessian equations
• Uniqueness properties of \(m\)-subharmonic functions in Cegrell classes
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• Maximal \(m\)-subharmonic functions and the Cegrell class \(\mathcal{N}_m\)
• A priori estimates for complex Hessian equations
• Weak solutions to the complex Hessian equation.
• Degenerate complex Hessian equations on compact Kahler manifolds
• On delta $m$-subharmonic functions
• Radial symmetric solution of complex Hessian equation in the unit ball
• The complex Monge–Ampère operator
• Monge–Ampère boundary measures
• Subsolution theorem for the complex Hessian equation
• Complex Hessian operator and Lelong number for unbounded m-subharmonic functions

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