Lectures on Convex Geometry by Wolfgang Weil

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.
Binding: Paperback / softback