For chi-plurisubharmonic solutions of complex Hessian equations with gradient-dependent right-hand sides on compact Hermitian manifolds, the second covariant derivative of the solution is uniformly bounded in terms of lower-order bounds and the data.
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Second order estimates for complex Hessian equations on Hermitian manifolds
For chi-plurisubharmonic solutions of complex Hessian equations with gradient-dependent right-hand sides on compact Hermitian manifolds, the second covariant derivative of the solution is uniformly bounded in terms of lower-order bounds and the data.