Harmonic mean curvature flow and geometric inequalities
Harmonic mean curvature flow and geometric inequalities
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DOI：
10.1016/j.aim.2020.107393
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发表时间：
2019-03
影响因子：
1.7
通讯作者：
B. Andrews;Yingxiang Hu;Haizhong Li
中科院分区：
文献类型：
--
作者：
B. Andrews;Yingxiang Hu;Haizhong Li
利用双曲空间中严格凸闭超曲面的调和平均曲率流，证明了关于总曲率（高斯曲率在超曲面上的积分）与quermass积分之间的Alexandrov-Fenchel型不等式。由此产生的不等式允许我们使用逆平均曲率流来证明严格凸超曲面的总曲率和面积之间的Alexandrov-Fenchel不等式。最后，我们应用调和平均曲率流证明了双曲空间中h-凸超曲面的一类新的几何不等式。
We employ the harmonic mean curvature flow of strictly convex closed hypersurfaces in hyperbolic space to prove Alexandrov-Fenchel type inequalities relating quermassintegrals to the total curvature, which is the integral of Gaussian curvature on the hypersurface. The resulting inequality allows us to use the inverse mean curvature flow to prove Alexandrov-Fenchel inequalities between the total curvature and the area for strictly convex hypersurfaces. Finally, we apply the harmonic mean curvature flow to prove a new class of geometric inequalities for h-convex hypersurfaces in hyperbolic space.