Lectures on Convex Geometry

This book provides a self-contained introduction to convex geometry in Euclidean space, covering basic concepts, Brunn-Minkowski theory, surface area measures, projection functions, zonoids, and geometric valuations. It is accessible to students in the third year and can be covered in one semester.

Format: Paperback / softback
Length: 287 pages
Publication date: 28 August 2021
Publisher: Springer Nature Switzerland AG

This comprehensive book offers a thorough introduction to convex geometry in Euclidean space, covering essential concepts and results. It delves into the Brunn-Minkowski theory, encompassing mixed volumes, the Brunn-Minkowski inequality, and its profound consequences, such as the isoperimetric inequality. The book also explores central topics like surface area measures, projection functions, zonoids, and geometric valuations. Additionally, it provides an insightful introduction to integral-geometric formulas in Euclidean space, complemented by numerous exercises and supplementary material. Designed for students in the third year, this text can be covered in a single semester, providing a solid foundation for further exploration in convex geometry and its applications.

Convexity, a fundamental and intuitive concept, holds immense importance in various mathematical disciplines, including functional analysis, optimization, probability theory, and stochastic geometry. This book serves as a gateway to the more advanced and specialized literature, making its content accessible to students in the third year and suitable for a one-semester course. By delving into essential concepts and results, this book provides a solid foundation for students to explore convex geometry and its applications further.

Weight: 474g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030501822
Edition number: 1st ed. 2020