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Lectures on Convex Geometry / / by Daniel Hug, Wolfgang Weil



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Autore: Hug Daniel Visualizza persona
Titolo: Lectures on Convex Geometry / / by Daniel Hug, Wolfgang Weil Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020
Edizione: 1st ed. 2020.
Descrizione fisica: 1 online resource (300 pages)
Disciplina: 516.08
Soggetto topico: Convex geometry 
Discrete geometry
Polytopes
Measure theory
Functional analysis
Convex and Discrete Geometry
Measure and Integration
Functional Analysis
Persona (resp. second.): WeilWolfgang
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Lectures on Convex Geometry  Visualizza cluster
ISBN: 3-030-50180-9
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910483883403321
Lo trovi qui: Univ. Federico II
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Serie: Graduate Texts in Mathematics, . 0072-5285 ; ; 286