Estimates for k-Hessian operator and some applications

DOI10.1007/s10587-013-0037-xzbMath1289.47126OpenAlexW2041316371MaRDI QIDQ2864429

Dongrui Wan

Publication date: 6 December 2013

Published in: Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10587-013-0037-x

zbMATH Keywords

\(k\)-Hessian operator\(k\)-Green function\(k\)-convex function\(k\)-Hessian measure

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Integration on manifolds; measures on manifolds (58C35) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15)

Related Items (5)

Quasicontinuity and maximality of quaternionic plurisubharmonic functions ⋮ 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 ⋮ \(m\)-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

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• Lelong-Jensen type formula, \(k\)-Hessian boundary measure and Lelong number for \(k\)-convex functions
• Jensen measures and boundary values of plurisubharmonic functions
• Potential estimates for a class of fully nonlinear elliptic equations.
• Hessian measures. III
• The general definition of the complex Monge-Ampère operator.
• Hessian measures. II
• Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function
• An energy estimate for the complex Monge-Ampère operator

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