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New Trends in Intuitive GeometryOn the Volume of Boolean Expressions of Balls – A Review of the Kneser–Poulsen Conjecture

New Trends in Intuitive Geometry: On the Volume of Boolean Expressions of Balls – A Review of the... [In 1954–55, E. T. Poulsen and M. Kneser formulated the conjecture that if some congruent balls of the Euclidean space are rearranged in such a way that the distances between the centers of the balls do not increase, then the volume of the union of the balls does not increase as well. Our goal is to give a survey of attempts to prove this conjecture, to discuss possible generalizations, and to collect some relevant open questions.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

New Trends in Intuitive GeometryOn the Volume of Boolean Expressions of Balls – A Review of the Kneser–Poulsen Conjecture

Part of the Bolyai Society Mathematical Studies Book Series (volume 27)
Editors: Ambrus, Gergely; Bárány, Imre; Böröczky, Károly J.; Fejes Tóth, Gábor ; Pach, János
Csikós, Balázs
New Trends in Intuitive Geometry — Nov 3, 2018
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Publisher
Springer Berlin Heidelberg
Copyright
© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018. Corrected Publication 2018
ISBN
978-3-662-57412-6
Pages
65 –94
DOI
10.1007/978-3-662-57413-3_4
Publisher site
See Chapter on Publisher Site

Abstract

[In 1954–55, E. T. Poulsen and M. Kneser formulated the conjecture that if some congruent balls of the Euclidean space are rearranged in such a way that the distances between the centers of the balls do not increase, then the volume of the union of the balls does not increase as well. Our goal is to give a survey of attempts to prove this conjecture, to discuss possible generalizations, and to collect some relevant open questions.]

Published: Nov 3, 2018

Keywords: Kneser–Poulsen conjecture; Volume inequalities; Variation of the volume; Schläfli formula; 52A40; 52A38; 26B20

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