A BRAY-BRENDLE-NEVES TYPE INEQUALITY FOR A RIEMANNIAN MANIFOLD

In this paper, for any local area-minimizing closed hypersurface Σ with ■, immersed in a（n + 1）-dimension Riemannian manifold M which has positive scalar curvature and nonnegative Ricci curvature, we obtain an upper bound for the area of Σ. In particular, when Σ saturates the corresponding upper bound, Σ is isometric to S;and M splits in a neighborhood of Σ. At the end of the paper, we also give the global version of this result.