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On the Volume of Boolean Expressions of Balls – A Review of the Kneser–Poulsen Conjecture

  • Balázs CsikósEmail author
Chapter
Part of the Bolyai Society Mathematical Studies book series (BSMS, volume 27)

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.

Keywords

Kneser–Poulsen conjecture Volume inequalities Variation of the volume Schläfli formula 

2010 Mathematics Subject Classification

52A40 52A38 26B20 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics, Eötvös UniversityBudapestHungary

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