Convex cones : geometry and probability / Rolf Schneider

Format:

Book

Author/Creator:

Schneider, Rolf, 1940- Author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2319.

Lecture Notes in Mathematics, 0075-8434 ; Volume 2319

Language:

English

Subjects (All):

Convex bodies.

Physical Description:

x, 347 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer Nature Switzerland AG, [2022]

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 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." -- Back cover

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.

Notes:

Includes bibliographical references (pages 329-337) and indexes.

Current copyright fee: GBP19.00 42\0.

Other Format:

Online version: Schneider, Rolf, 1940- Convex cones.

ISBN:

9783031151262

3031151267

OCLC:

1336536900