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＜E-Book＞
Lectures on Convex Geometry / by Daniel Hug, Wolfgang Weil
(Graduate Texts in Mathematics. ISSN:21975612 ; 286)

Edition	1st ed. 2020.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2020
Language	English
Size	XVIII, 287 p. 11 illus., 9 illus. in color : online resource
Authors	*Hug, Daniel author Weil, Wolfgang author SpringerLink (Online service)
Subjects	LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Polytopes LCSH:Measure theory LCSH:Functional analysis FREE:Convex and Discrete Geometry FREE:Polytopes FREE:Measure and Integration FREE:Functional Analysis
Notes	Preface -- Preliminaries and Notation -- 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 -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/978-3-030-50180-8

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