ON THE VOLUME OF THE UNION OF BALLS

Authors
CSIKOS B
Citation
B. Csikos, ON THE VOLUME OF THE UNION OF BALLS, Discrete & computational geometry, 20(4), 1998, pp. 449-461
Citations number
11
Categorie Soggetti
Computer Science Theory & Methods",Mathematics,"Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
20
Issue
4
Year of publication
1998
Pages
449 - 461
Database
ISI
SICI code
0179-5376(1998)20:4<449:OTVOTU>2.0.ZU;2-Z
Abstract
We prove that if some balls in the Euclidean space move continuously i n such a way that the distances between their centers decrease, then t he volume of their union cannot increase. The proof is based on a form ula expressing the derivative of the volume of the union as a linear c ombination of the derivatives of the distances between the centers wit h nonnegative coefficients.