Lectures on convex geometry [Documento eletrónico] / by Daniel Hug, Wolfgang Weil
Language: eng.Country: Switzerland, Swiss Confederation.Publication: Cham : Springer International Publishing, Springer, 2020Description: XVIII, 287 p. : il.ISBN: 978-3-030-50180-8.Series: Graduate Texts in Mathematics, 286Subject - Topical Name: Convex geometry | Discrete geometry | Polytopes | Measure theory | Functional analysis Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA639.5.SPR FCT (Browse shelf(Opens below)) | 1 | Available | 96046 |
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.
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