| Dewey Class |
516.1 |
| Title |
Lectures on Convex Geometry ([EBook]) / by Daniel Hug, Wolfgang Weil. |
| Author |
Hug, Daniel |
| Added Personal Name |
Weil, Wolfgang |
| Other name(s) |
SpringerLink (Online service) |
| Edition statement |
1st ed. 2020. |
| Publication |
Cham : : Springer International Publishing : : Imprint: Springer, , 2020. |
| Physical Details |
XVIII, 287 p. 11 illus., 9 illus. in color. : online resource. |
| Series |
Graduate texts in mathematics 0072-5285 ; ; 286 |
| ISBN |
9783030501808 |
| Summary Note |
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.: |
| Contents note |
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. |
| Mode of acces to digital resource |
Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format |
| System details note |
- Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users). |
| Internet Site |
https://doi.org/10.1007/978-3-030-50180-8 |
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