Gradient estimates for Monge–Ampère type equations on compact almost Hermitian manifolds with boundary

We investigate Monge–Ampère type fully nonlinear equations on compact almost Hermitian manifolds with boundary and show a priori gradient estimates for a smooth solution of these equations.

On the k-th almost Gauduchon condition on almost Hermitian manifolds

We introduce the k-th almost Gauduchon condition on almost Hermitian manifolds. We show that if there is a k-th almost Gauduchon metric for some k, then it is k-th almost Gauduchon for any other k.