Lelong-Jensen type formula, \(k\)-Hessian boundary measure and Lelong number for \(k\)-convex functions

DOI10.1016/J.MATPUR.2012.10.002zbMath1280.35029OpenAlexW1978761661MaRDI QIDQ387974

Dongrui Wan, Wei Wang

Publication date: 18 December 2013

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2012.10.002

zbMATH Keywords

pluripotential theoryfully nonlinear elliptic equations\(k\)-Hessian operatorviscosity subsolutions

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Complex Monge-Ampère operators (32W20) Viscosity solutions to PDEs (35D40) Comparison principles in context of PDEs (35B51)

Related Items (10)

Weighted Green functions for complex Hessian operators ⋮ The geometry of \(m\)-hyperconvex domains ⋮ Quasicontinuity and maximality of quaternionic plurisubharmonic functions ⋮ Quaternionic Monge-Ampère operator for unbounded plurisubharmonic functions ⋮ Lelong–Jensen formula, Demailly–Lelong numbers and weighted degree of positive supercurrents ⋮ Complex Hessian operator and generalized Lelong numbers associated to a closed \(m\)-positive current ⋮ Complex Hessian operator and Lelong number for unbounded m-subharmonic functions ⋮ Estimates for k-Hessian operator and some applications ⋮ \(m\)-potential theory and \(m\)-generalized Lelong numbers associated with \(m\)-positive supercurrents ⋮ On the quaternionic Monge-Ampère operator, closed positive currents and Lelong-Jensen type formula on the quaternionic space

Cites Work

• A new capacity for plurisubharmonic functions
• Mesures de Monge-Ampère et mesures pluriharmoniques. (Monge-Ampère measures and pluriharmonic measures)
• Hessian measures. I
• The Dirichlet problem for a complex Monge-Ampère equation
• Potential estimates for a class of fully nonlinear elliptic equations.
• Hessian measures. III
• Hessian measures. II
• Weak solutions to the complex Hessian equation.
• The k-Hessian Equation
• Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines
• The domain of definition of the complex Monge-Ampere operator
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