Fully non-linear degenerate elliptic equations in complex geometry

We derive an a priori real Hessian estimate for solutions of large family geometric fully non-linear elliptic equations on compact Hermitian manifolds, which is independent lower bound the right-hand side function. This improves estimates Székelyhidi [57] and additionally applies to with degenerate side. As application, we establish optimal C1,1 regularity envelopes (?,m)-subharmonic functions manifolds.