Convex Cones

Rolf Schneider is Professor Emeritus at the University of Freiburg. He obtained his PhD in 1967 (Frankfurt) and his Habilitation in 1969 (Bochum), after which he was Assistant Professor at the University of Frankfurt (1970) and then Full Professor at Technische Universitat Berlin (1970) and the University of Freiburg (1974). He became Professor Emeritus in 2005. He is an Honorary Doctor of the University of Salzburg and a Fellow of the American Mathematical Society. With research interests primarily in convex geometry and stochastic geometry, he has over 200 publications, including the books Convex Bodies: The Brunn-Minkowski Theory and (with Wolfgang Weil) Stochastic and Integral Geometry.

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.

"Convex cones: geometry and probability stands out in the present literature as probably the first and only textbook entirely dedicated to the development of the theory of convex cones ... . Given the self-contained nature of the presentation and the number of results and research directions that are touched upon ... this book seems bound to serve as a useful reference point for a number of research mathematicians in the years to come." (Giorgos Chasapis, Mathematical Reviews, December, 2023)

"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)

“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)