Slicing convex sets and measures by a hyperplane

被引：18
|
作者：
Barany, Imre [1 ,2 ]
Hubard, Alfredo [3 ]
Jeronimo, Jesus [4 ]
机构：
[1] Hungarian Acad Sci, Renyi Inst Math, H-1364 Budapest, Hungary
[2] UCL, Dept Math, London WC1E 6BT, England
[3] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City 04510, DF, Mexico
[4] Ctr Invest Matemat AC, Guanajuato, Mexico
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2008年 / 39卷 / 1-3期
关键词：
convex bodies; well separated families; sections of convex sets and measures;
D O I：
10.1007/s00454-007-9021-2
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Given convex bodies K(1), ..., K (d) in R(d) supercript stop and numbers alpha (1), ..., alpha (d) is an element of [0,1], we give a sufficient condition for existence and uniqueness of an (oriented) halfspace H with Vol(H boolean AND K(i) )=alpha (i) . VolK(i) for every i. The result is extended from convex bodies to measures.
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页码：67 / 75
页数：9
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