Stable Type Solutions of the Complex Laplacian Operators on Hermitian Manifolds

In this paper, we investigate the rigidity properties of stable type solutions of the complex Laplacian operators on Hermitian manifolds with Gauduchon metric, which has been considered for the Laplace–Beltrami operators on Riemannian manifolds by other authors. We derive some integral inequalities involving Chern curvature tensor about stable type solutions and the Liouville type results for the stable type solutions under assuming some curvature signs.