03643nam 22006735 450 99641827150331620221219230947.03-030-50180-910.1007/978-3-030-50180-8(OCoLC)1192490338(CKB)4100000011401198(MiAaPQ)EBC6320837(DE-He213)978-3-030-50180-8(PPN)250214938(EXLCZ)99410000001140119820210806h2020 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierLectures on Convex Geometry[electronic resource] /by Daniel Hug, Wolfgang Weil1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (300 pages)Graduate Texts in Mathematics,0072-5285 ;2863-030-50179-5 Includes bibliographical references and index.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.Graduate Texts in Mathematics,0072-5285 ;286Convex geometry Discrete geometryPolytopesMeasure theoryFunctional analysisConvex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014Polytopeshttps://scigraph.springernature.com/ontologies/product-market-codes/M21040Measure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Convex geometry .Discrete geometry.Polytopes.Measure theory.Functional analysis.Convex and Discrete Geometry.Polytopes.Measure and Integration.Functional Analysis.516.08Hug Danielauthttp://id.loc.gov/vocabulary/relators/aut1065686Weil Wolfgangauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996418271503316Lectures on Convex Geometry2547512UNISA