Splitting and pinching for convex sets

被引：0

作者：

Kohlmann, P ^{[1
]}

机构：

[1] UNIV DORTMUND,INST MATH,D-44221 DORTMUND,GERMANY

来源：

GEOMETRIAE DEDICATA | 1996年 / 60卷 / 02期

关键词：

convex sets; orthogonal disc cylinders; splitting property;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider noncompact, closed and convex sets with nonvoid interior in Euclidean space. It is shown that if such a set has one curvature measure sufficiently close to the boundary measure, then it is congruent to a product of a vector space and a compact convex body. Related stability and characterization theorems for orthogonal disc cylinders are proved. Our arguments are based on the Steiner-Schwarz symmetrization processes and generalized Minkowski integral formulas.

引用

页码：125 / 143

页数：19

共 18 条

[1]

[Anonymous], ENCY MATH ITS APPL

[2]

Federer H., 1959, Trans. Amer. Math. Soc., V93, P418, DOI [DOI 10.1090/S0002-9947-1959-0110078-1, 10.1090/S0002-9947-1959-0110078-1, DOI 10.2307/1993504]

[3] ON SPHERICAL IMAGE MAPS WHOSE JACOBIANS DO NOT CHANGE SIGN [J].