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

页码：345 / 373

页数：29

共 35 条

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