Volume Inequalities for Arrangements of Convex Bodies

The book is centered around two major conjectures of discrete geometry: the Hadwiger-Levi conjecture (1955) and the Kneser-Poulsen conjecture (1955). Although both conjectures have been solved only in dimension two and are open in higher dimensions, they have already influenced a great deal of research in discrete geometry and surely will continue to do so. The book gives a detailed account of all major results already achieved with complete proofs and emphasizing the role of volumetric methods/inequalities. The book’s main purpose is to present the relevant frontline research in discrete geometry while generating wider interest in two fundamental conjectures of discrete geometry.

Karoly Bezdek is a Professor and Director - Centre for Computational & Discrete Geometry,

Pure Mathematics at University of Calgary. He received his Ph.D. in mathematics at the ELTE University of

Budapest. He holds a first tier Canada chair, which is the highest level

of research funding awarded by the government of Canada