Hausdorff Dimension of the Set of Endpoints of Typical Convex Surfaces

被引：0

作者：

Riviere, Alain ^{[1
]}

机构：

[1] CNRS, UMR 7352, Fac Sci Amiens, Lab Amienois Math Fondamentales & Appl, F-80039 Amiens 1, France

来源：

JOURNAL OF CONVEX ANALYSIS | 2015年 / 22卷 / 02期

关键词：

Cut locus; Hausdorff dimension; convex body; SPACES; CURVATURE;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We mainly prove that most d-dimensional convex surfaces Sigma have a set of endpoints of Hausdorff dimension at least d/3. An endpoint means a point not lying in the interior of any shorter path in Sigma. "Most" means that the exceptions constitute a meager set, relatively to the usual Hausdorff-Pompeiu distance. The proof employs some of the ideas used in [9] about a similar question. However, our result here is just an estimation about a still unsolved question, as much as we know.

引用

页码：541 / 551

页数：11

共 15 条

[1]

Adiprasito K, 2012, J CONVEX ANAL, V19, P385

[2] Infinite curvature on typical convex surfaces [J].