Modulus of continuity for solutions to complex Monge-Ampère equations on Hermitian manifolds

2025/10/26 by Liu, Junbang
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.22774

Abstract

In this note, we give a proof of the uniform log-continuity of the solution to complex Monge-Ampère equations on compact Hermitian manifolds, which is a generalization of the result of Guo-Phong-Tong-Wang in the Kähler case.

Citations

• Continuity of solutions to complex Hessian equations on compact Hermitian manifolds
• Complex Alexandrov-Bakelman-Pucci estimate and its applications
• Viscosity solution to complex Hessian equations on compact Hermitian manifolds
• Sup-slopes and sub-solutions for fully nonlinear elliptic equations
• Regularization Of m-subharmonic Functions And HÖlder Continuity
• On the modulus of continuity of solutions to complex Monge-Ampère equations
• Stability and Hölder regularity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds
• Regularity of plurisubharmonic upper envelopes in big cohomology classes

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