For admissible, chi-semi-convex solutions of complex Hessian equations with gradient terms on compact Hermitian manifolds, the paper proves uniform second-order estimates.
Cherrier, ´Equations de Monge-Amp` ere sur les vari´ et´ es Hermitiennes compactes, Bull
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Second order estimates for $\chi$-semi convex solutions of Hessian equations on Hermitian manifolds
For admissible, chi-semi-convex solutions of complex Hessian equations with gradient terms on compact Hermitian manifolds, the paper proves uniform second-order estimates.