Lectures on convex geometry
Material type:
TextSeries: Graduate texts in mathematics ; 286.Publication details: Switzerland : Springer Nature, 2020. Description: xviii, 287pISBN: 9783030501792Subject(s): Convex geometry | Algebraic geometry | Convex and Discrete Geometry | Discrete geometry | Functional analysis & transforms | Geometry | Integral calculus & equations | Brunn-Minkowski theory | Integral geometry | Measure theoryDDC classification: 514.17 Online resources: Table of contents | Reviews 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
NBHM Books
|
SMS Library | 514.17 HUG-L (Browse shelf(Opens below)) | Available | N435 |
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| 514.152.6 SHU-P Points and lines: characterizing the classical geometries | 514.161 UEB-F Foundations of incidence geometry: projective and polar spaces | 514.17 BER-C Convex optimization theory | 514.17 HUG-L Lectures on convex geometry | 514.17 MAT-L Lectures on discrete geometry | 514.172.2 ABA-C Curves and surfaces | 514.172.4 SCH-C Convex bodies: the brunn-Minkowski theory |
Includes bibliographical references and 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.
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