Some almost-Schur type inequalities and applications on sub-static manifolds

Abstract

In this paper, we establish some almost-Schur type inequalities on sub-static manifolds, naturally arising in General Relativity. In particular, our results generalize those in [1] of Li-Xia for r-th mean curvatures of closed sub-static hypersurfaces in space forms and k-scalar curvatures for closed locally conformally flat sub-static manifolds. Moreover, our results also generalize those of Cheng [2].

Keywords

• almost-schur type inequalities
• sub-static manifolds
• mean curvature
• ricci curvature