Infinite curvature on typical convex surfaces

被引：4

作者：

Adiprasito, Karim ^{[1
]}

机构：

[1] Free Univ Berlin, Berlin, Germany

来源：

GEOMETRIAE DEDICATA | 2012年 / 159卷 / 01期

关键词：

Baire category; Convex body; Typical; Curvature; Umbilical points;

D O I：

10.1007/s10711-011-9658-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Solving a long-standing open question of Zamfirescu, we will show that typical convex surfaces contain points of infinite curvature in all tangent directions. To prove this, we use an easy curvature definition imitating the idea of Alexandrov spaces of bounded curvature, and show continuity properties for this notion.

引用

页码：267 / 275

页数：9

共 10 条

[1]

Adiprasito K., J CONVEX AN IN PRESS

[2]

Busemann H., 2008, CONVEX SURFACES

[3] MOST CONVEX FIELDS ARE SMOOTH, BUT NOT TOO SMOOTH [J].