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Volume Inequalities for Arrangements of Convex Bodies

Karoly Bezdek, Muhammad Ali Khan (Autoren)

Buch | Hardcover

304 Seiten

2021
Productivity Press (Verlag)
978-1-4987-4378-5 (ISBN)

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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

Volume Inequalities for Coverings - the influence of the Hadwiger-Levi Conjecture (1955). On the density and symmetry of covering Euclidean d-space by translates of a convex body. Covering numbers and weighted coverings – volumetric estimates. The Hadwiger-Levi conjecture and its equivalent formulations. The status of the Hadwiger-Levi conjecture: progress and results for covering by smaller homothets in dimensions two and higher. A computer based approach. Quantifying covering and illumination: the covering and illumination parameters of convex bodies. The vertex and covering indices of convex bodies – volumetric estimates. X-raying and covering by planks and cylinders. Volume Inequalities for Sphere Arrangements – the influence of the Kneser-Poulsen Conjecture (1955). Theorems of Kirszbraun, Kneser and Brehm. The status of the Kneser-Poulsen conjecture. Aspects of the Kneser-Poulsen conjecture.

Erscheint lt. Verlag	1.1.2021
Reihe/Serie	Discrete Mathematics and Its Applications
Zusatzinfo	50 Illustrations, black and white
Verlagsort	Portland
Sprache	englisch
Maße	156 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	1-4987-4378-1 / 1498743781
ISBN-13	978-1-4987-4378-5 / 9781498743785
Zustand	Neuware