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Lectures on Convex Geometry / by Daniel Hug, Wolfgang Weil

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Graduate Texts in Mathematics ; 286 | Springer eBook CollectionPublisher: Cham : Springer International Publishing, 2020Publisher: Cham : Imprint: Springer, 2020Edition: 1st ed. 2020Description: 1 Online-Ressource(XVIII, 287 p. 11 illus., 9 illus. in color.)ISBN:
  • 9783030501808
Subject(s): Additional physical formats: 9783030501792 | 9783030501815 | 9783030501822 | Erscheint auch als: 9783030501792 Druck-Ausgabe | Erscheint auch als: 9783030501815 Druck-Ausgabe | Erscheint auch als: 9783030501822 Druck-AusgabeDOI: DOI: 10.1007/978-3-030-50180-8Online resources: Summary: 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.Summary: 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.PPN: PPN: 1728471419Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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