ALEXANDROV-FENCHEL INEQUALITIES FOR CONVEX HYPERSURFACES WITH FREE BOUNDARY IN A BALL

被引：2
|
作者：
Scheuer, Julian [1 ]
Wang, Guofang [2 ]
Xia, Chao [3 ]
机构：
[1] Cardiff Univ, Sch Math, Senghennydd Rd, Cardiff CF24 4AG, Wales
[2] Albert Ludwigs Univ, Math Inst, Abt Reine Math, Ernst Zermelo Str 1, D-79104 Freiburg, Germany
[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
JOURNAL OF DIFFERENTIAL GEOMETRY | 2022年 / 120卷 / 02期
关键词：
Free boundary hypersurface; quermassintegral; inverse curvature flow; constrained curvature flow; geometric inequality; MEAN-CURVATURE FLOW; VOLUME PRESERVING FLOW; MINIMAL-SURFACES; HYPERBOLIC SPACE;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we first introduce quermassintegrals for free boundary hypersurfaces in the (n + 1)-dimensional Euclidean unit ball. Then we solve some related isoperimetric type problems for convex free boundary hypersurfaces, which lead to new Alexandrov-Fenchel inequalities. In particular, for n = 2 we obtain a Minkowski-type inequality and for n = 3 we obtain an optimal Willmore-type inequality. To prove these estimates, we employ a specifically designed locally constrained inverse harmonic mean curvature flow with free boundary.
引用
收藏
页码：345 / 373
页数：29
相关论文
共 35 条
1234