On the regularity of the complex Hessian equation

DOI10.1090/proc/16042zbMath1504.32087arXiv2110.02620OpenAlexW4214858434MaRDI QIDQ5039254

Per Åhag, Rafał Czyż

Publication date: 12 October 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.02620

zbMATH Keywords

stabilitypluripotential theory\(m\)-subharmonic function\((\omega,m)\)-subharmonic function

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Nonlinear elliptic equations (35J60) Other generalizations (nonlinear potential theory, etc.) (31C45) Plurisubharmonic functions and generalizations (32U05) Notions of stability for complex manifolds (32Q26)

Cites Work

• Capacities and Hessians in the class of \(m\)-subharmonic functions
• Potential theory in the class of \(m\)-subharmonic functions
• Hölder continuous solutions to complex Hessian equations
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• The Dirichlet problem for the complex Monge-Ampère operator: Stability in \(L^ 2\)
• Pluricomplex energy
• The complex Monge-Ampère equation
• The geometry of \(m\)-hyperconvex domains
• Viscosity solutions to complex Hessian equations
• On a family of quasimetric spaces in generalized potential theory
• Poincaré- and Sobolev- type inequalities for complex \(m\)-Hessian equations
• Plurisubharmonic envelopes and supersolutions
• Mixed Hessian inequalities and uniqueness in the class \(\mathcal {E}(X,\omega ,m)\)
• A variational approach to complex Hessian equations in \(\mathbb{C}^n\)
• Maximal \(m\)-subharmonic functions and the Cegrell class \(\mathcal{N}_m\)
• The equation of complex Monge-Ampère type and stability of solutions
• A priori estimates for complex Hessian equations
• Weak solutions to the complex Hessian equation.
• Degenerate complex Hessian equations on compact Kahler manifolds
• Modulus of continuity of solutions to complex Hessian equations
• On delta $m$-subharmonic functions
• An Inequality Between Complex Hessian Measures of Hölder Continuous m-subharmonic Functions and Capacity
• Nonlinear elliptic equations and the complex hessian
• Complex Hessian equations with prescribed singularity on compact Kähler manifolds
• On the regularity of complex Hessian equation on m-hyperconvex domain