Convex Cones : Geometry and Probability - Rolf Schneider

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Convex Cones

Geometry and Probability

By: Rolf Schneider

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Paperback | 22 September 2022

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Paperback
360 Pages

Dimensions(cm)
23.5 x 15.5 x 1.91

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This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn-Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and Grassmann angles, and develops general versions of the relevant formulas, namely the Steiner formula and kinematic formula.

In recent years questions related to convex cones have arisen in applied mathematics, involving, for example, properties of random cones and their non-trivial intersections. The prerequisites for this work, such as integral geometric formulas and results on conic intrinsic volumes, were previously scattered throughout the literature, but no coherent presentation was available. The present book closes this gap. It includes several pearls from the theory of convex cones, which should be better known.

Industry Reviews

"This book develops the necessary machinery for geometric applications of convex cones. The concise style and wealth of references and ideas make this book without doubt a valuable source of information. Each chapter of the book starts with an overview that outlines the main ideas and results. Moreover, each section finishes with a list of notes containing further references, open problems and extensions of presented results." (Florian Pausinger, zbMATH 1505.52001, 2023)

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