Alexandrov-Fenchel type inequalities in the sphere

In this paper, we attempt to use two types of flows to study the relations between quermassintegrals $\mathcal{A}_k$ (see Definition 1.1), which correspond to the Alexandrov-Fenchel inequalities for closed convex $C^2$-hypersurfaces in $\mathbb{S}_+^{n+1}.$

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