当前位置: X-MOL 学术J. Differ. Geom. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball
Journal of Differential Geometry ( IF 2.5 ) Pub Date : 2022-02-01 , DOI: 10.4310/jdg/1645207496
Julian Scheuer 1 , Guofang Wang 2 , Chao Xia 3
Affiliation  

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.

中文翻译:

球中具有自由边界的凸超曲面的 Alexandrov-Fenchel 不等式

在本文中,我们首先介绍了 $(n+1)$ 维欧几里得单位球中自由边界超曲面的 quermassintegrals。然后我们解决了凸自由边界超曲面的一些相关等周类型问题,这些问题导致了新的 Alexandrov-Fenchel 不等式。特别是,对于 $n=2$,我们得到一个 Minkowski 型不等式,对于 $n=3$,我们得到一个最优 Willmore 型不等式。为了证明这些估计,我们采用了专门设计的具有自由边界的局部约束逆谐波平均曲率流。
更新日期:2022-02-01
down
wechat
bug