Convex cones: geometry and probability
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 BrunnMinkowski 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 rel…
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- Full title :Convex cones : geometry and probability / Rolf Schneider.
Summary
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 BrunnMinkowski 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. .
Read More ↓Edition Statements
- Publication Date:©2022
Publication Statements
- Publisher(s):Springer
- Place of Publication:Cham
- Language:eng
- Publication Date:©2022
The Physical Object
- Description:1 online resource (x, 347 pages) : : illustrations.
Edition Identifiers
- ISBN:9783031151279, 3031151275
- DOI:10.1007/978-3-031-15127-9
- oclc:on1345582392
- LC Classification:QA639.5
- Dewey Decimal:516/.08
Table of Contents
Basic notions and facts -- Angle functions -- Relations to spherical geometry -- Steiner and kinematic formulas -- Central hyperplane arrangements and induced cones -- Miscellanea on random cones -- Convex hypersurfaces adapted to cones.
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