ALEXANDROV-FENCHEL TYPE INEQUALITIES IN THE SPHERE
ALEXANDROV-FENCHEL TYPE INEQUALITIES IN THE SPHERE
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发表时间：
2017
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通讯作者：
M. Makowski;Julian Scheuer
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作者：
M. Makowski;Julian Scheuer
我们证明了一个刚性的结果，使我们能够推广的结果光滑凸超曲面在球上做CarmoWarner凸C-超曲面。我们应用这些结果证明了嵌入的，封闭的，严格凸的初始超曲面的反F -曲率流的C收敛性。这一结果适用于大类曲率函数，包括平均曲率和高斯曲率的任意幂。利用这个结果证明了球面上的Alexandrov-Fenchel型不等式。
We prove a rigidity result in the sphere which allows us to generalize a result about smooth convex hypersurfaces in the sphere by Do CarmoWarner to convex C-hypersurfaces. We apply these results to prove Cconvergence of inverse F -curvature flows in the sphere to an equator in S for embedded, closed, strictly convex initial hypersurfaces. The result holds for large classes of curvature functions including the mean curvature and arbitrary powers of the Gauss curvature. We use this result to prove Alexandrov-Fenchel type inequalities in the sphere.