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We obtain a priori $L^\infty$ estimate for a general class of $(n-1)-$formfully nonlinear partial differential equations on compact Hermitian manifolds.Our method relies on the local version of comparison with auxiliaryMonge-Amp\`ere equations, developed earlier by B. Guo and D. H. Phong. The keyis to find the appropriate elliptic operator such that the maximum principleapplies.

On uniform estimates for $(n-1)-$form fully nonlinear partial differential equations on compact Hermitian manifolds