A Weak Solution to the Complex Hessian Equation Associated to an m-Positive Closed Current

DOI10.15407/MAG18.01.118zbMath1495.32087OpenAlexW4223955149MaRDI QIDQ5087703

Jawhar Hbil, Mohamed Zaway

Publication date: 1 July 2022

Published in: Zurnal matematiceskoj fiziki, analiza, geometrii (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.15407/mag18.01.118

zbMATH Keywords

capacity\(m\)-subharmonic functionHessian operator\(m\)-positive closed current

Mathematics Subject Classification ID

Plurisubharmonic functions and generalizations (32U05) Currents (32U40) Capacity theory and generalizations (32U20)

Cites Work

• Potential theory in the class of \(m\)-subharmonic functions
• Lelong-Demailly numbers in terms of capacity and weak convergence for closed positive currents
• A new capacity for plurisubharmonic functions
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• Capacity associated to a positive closed current
• A priori estimates for complex Hessian equations
• Weak solutions to the complex Hessian equation.
• Approximation of Plurisubharmonic Functions and the Dirichlet Problem for the Complex Monge-Ampère Operator.
• Continuity of the complex Monge-Ampère operator
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