TY  - BOOK
AU  - Hug, Daniel
AU  - Weil, Wolfgang
TI  - Lectures on Convex Geometry
T2  - Graduate Texts in Mathematics 
SN  - 9783030501792 (PB)
PY  - 2020///
CY  - Cham
PB  - Springer
KW  - Convexity
KW  - Convex and Discrete Geometry
KW  - Measure and Integration
N1  - Includes References (281-284) and Index;     1. Convex Sets 
    2. Convex Functions
    3. Brunn-Minkowski Theory
    4. From Area Measures to Valuations 
    5. Integral-Geometric Formulas 
    6. Solutions of Selected Exercises
N2  - This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
ER  -