Abstract
By improving the analysis developed in the study of σk-Yamabe problem, we prove in this paper the following new inequality for any 3-dimensional Riemannian manifold (M3,g) of non-negative scalar curvature(∫Mσ1(g)dv(g))2⩾3vol(g)∫Mσ2(g)dv(g). Equality holds if and only if (M3,g) is a space form.
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