On the volume of the union of balls

被引：27

作者：

Csikos, B ^{[1
]}

机构：

[1] Eotvos Lorand Univ, Dept Geometry, H-1088 Budapest, Hungary

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 1998年 / 20卷 / 04期

关键词：

Linear Combination; Euclidean Space; Space Move; Nonnegative Coefficient;

D O I：

10.1007/PL00009395

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that if some balls in the Euclidean space move continuously in such a way that the distances between their centers decrease, then the volume of their union cannot increase. The proof is based on a formula expressing the derivative of the volume of the union as a linear combination of the derivatives of the distances between the centers with nonnegative coefficients.

引用

页码：449 / 461

页数：13