Abstract
In this paper, we proved the Alexandrov-Fenchel inequalities for embedded, closed, connected and convex C2-hypersurfaces in Sn+1: Ak≥ξk,k−2(Ak−2) for any 1≤k≤n−1, where Ak is the quermassintegral (see Definition 1.1) and ξk,k−2 is the unique positive function such that the equality holds when M is a geodesic sphere.
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