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Lectures on convex geometry

Hug, Daniel.

Lectures on convex geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on convex geometryby Daniel Hug, Wolfgang Weil.
Author:	Hug, Daniel.
other author:	Weil, Wolfgang.
Published:	Cham :Springer International Publishing :2020.
Description:	xviii, 287 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Convex geometry.
Online resource:	https://doi.org/10.1007/978-3-030-50180-8
ISBN:	9783030501808$q(electronic bk.)

Lectures on convex geometry
Hug, Daniel.

Lectures on convex geometry[electronic resource] /by Daniel Hug, Wolfgang Weil. - Cham :Springer International Publishing :2020. - xviii, 287 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2860072-5285 ;. - Graduate texts in mathematics ;129..

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.

ISBN: 9783030501808$q(electronic bk.)

Standard No.: 10.1007/978-3-030-50180-8doiSubjects--Topical Terms:

187435
Convex geometry.

LC Class. No.: QA639.5

Dewey Class. No.: 516.08

Lectures on convex geometry
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245 1 0 $a Lectures on convex geometry $h [electronic resource] / $c by Daniel Hug, Wolfgang Weil.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xviii, 287 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 286
505 0 $a 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.
520 $a 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.
650 0 $a Convex geometry. $3 187435
650 1 4 $a Convex and Discrete Geometry. $3 277230
650 2 4 $a Polytopes. $3 205957
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Functional Analysis. $3 274845
700 1 $a Weil, Wolfgang. $3 306355
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773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-030-50180-8
950 $a Mathematics and Statistics (SpringerNature-11649)