Cutting the Same Fraction of Several Measures

被引：6

作者：

Akopyan, Arseniy ^{[1
,2
]}

Karasev, Roman ^{[2
,3
]}

机构：

[1] RAS, Inst Informat Transmiss Problems, Moscow 127994, Russia

[2] PG Demidov Yaroslavl State Univ, BN Delone Int Lab Discrete & Computat Geometry, Yaroslavl 150000, Russia

[3] Moscow Inst Phys & Technol, Dept Math, Dolgoprudnyi 141700, Russia

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2013年 / 49卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

The ham sandwich theorem; Balanced partition; SETS;

D O I：

10.1007/s00454-012-9450-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study some measure partition problems: Cut the same positive fraction of d+1 measures in a"e (d) with a hyperplane or find a convex subset of a"e (d) on which d+1 given measures have the same prescribed value. For both problems positive answers are given under some additional assumptions.

引用

页码：402 / 410

页数：9

共 15 条

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[Anonymous], 2003, USING BORSUK ULAM TH

[2]

[Anonymous], 1942, DUKE MATH J, DOI 10.1215/S0012-7094-42-00925-6

[3]

Aronov B., 2010, ARXIV10104611

[4] Using equivariant obstruction theory in combinatorial geometry [J].