A characterization of the Cegrell classes and generalized $m$-capacities

DOI10.4064/ap170728-26-1zbMath1422.32032OpenAlexW2808879673MaRDI QIDQ4581971

van Thien Nguyen

Publication date: 21 August 2018

Published in: Annales Polonici Mathematici (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/ap170728-26-1

zbMATH Keywords

capacitysublevel set\(m\)-subharmonic functionscomplex Hessian equationsCegrell class

Mathematics Subject Classification ID

Plurisubharmonic functions and generalizations (32U05) General pluripotential theory (32U15) Capacity theory and generalizations (32U20) Plurisubharmonic exhaustion functions (32U10)

Related Items (8)

A note on the space of delta \(m\)-subharmonic functions ⋮ Maximal \(m\)-subharmonic functions and the Cegrell class \(\mathcal{N}_m\) ⋮ An Inequality Between Complex Hessian Measures of Hölder Continuous m-subharmonic Functions and Capacity ⋮ Complex Hessian operator associated to an \(m\)-positive closed current and weighted \(m\)-capacity ⋮ Poincaré- and Sobolev- type inequalities for complex \(m\)-Hessian equations ⋮ Decay near boundary of volume of sublevel sets of \(m\)-subharmonic functions ⋮ On the weighted \(m\)-energy classes ⋮ \(m\)-potential theory and \(m\)-generalized Lelong numbers associated with \(m\)-positive supercurrents

Cites Work

• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• A priori estimates for complex Hessian equations
• Hessian measures on m-polar sets and applications to the complex Hessian equations
• Subsolution theorem for the complex Hessian equation

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