【摘 要】
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In this paper,for any local area-minimizing closed hypersurface ∑ with RcΣ =RΣ/ngΣ,immersed in a (n + 1)-dimension Riemannian manifold M which has positive
【机 构】
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School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China
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In this paper,for any local area-minimizing closed hypersurface ∑ with RcΣ =RΣ/ngΣ,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 ∑.In particular,when ∑ saturates the corresponding upper bound,∑ is isometric to Sn and M splits in a neighborhood of ∑.At the end of the paper,we also give the global version of this result.
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