Convexity from the Geometric Point of ViewExercises and Solutions

This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View , published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding solutions follow each exercise. Besides the discussion of all solutions, some additional facts about the main text are sprinkled throughout. Sections of further reading are posted to the ends of each chapter supplying the reader with background literature to selected notions and tools that play a role in the exercises and/or solutions to the chapter.

The original text gives a comprehensive introduction to the common core of convex geometry and is suitable as a primary text for courses in convex geometry and in discrete geometry (including polytopes). Additionally, it can be used as a single reference for a complete introduction to convex geometry. The content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field, various subfields, and interesting connections to neighboring disciplines. Mainly directed to graduate and advanced undergraduates, the original text is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. The same is true for this book of solutions.

Designed for Instructors, graduate students, and independent learners Contains all the exercises from the main text followed by their respective solutions Solutions are often detailed with multiple references to results found in the main text

Contenu

Exercises & Solutions Convex functions.- Exercises & Solutions Convex sets.- Exercises & Solutions A first look into polytopes.- Exercises & Solutions Volume and area.- Exercises & Solutions Classical inequalities.- Exercises & Solutions Mixed volumes.- Exercises & Solutions Mixed surface area measures.- 8. Exercises & Solutions The Alexandrov-Fenchel inequality.- Exercises & Solutions Affine convex geometry I .- Exercises & Solutions Affine convex geometry II.- Exercises & Solutions Further selected topics.- Exercises & Solutions Historical steps of development of convexity as a field.