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Lectures on convex geometry

Hug, Daniel.

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Lectures on convex geometry

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on convex geometry/ by 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.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Convex geometry. -
Online resource:	https://doi.org/10.1007/978-3-030-50180-8
ISBN:	9783030501808

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 ;286..

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

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

567300
Convex geometry.

LC Class. No.: QA639.5

Dewey Class. No.: 516.08

Lectures on convex geometry
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100 1 $a Hug, Daniel. $3 3526037
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 567300
650 1 4 $a Convex and Discrete Geometry. $3 893686
650 2 4 $a Polytopes. $3 704968
650 2 4 $a Measure and Integration. $3 891263
650 2 4 $a Functional Analysis. $3 893943
700 1 $a Weil, Wolfgang. $3 923966
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Graduate texts in mathematics ; $v 286. $3 3526038
856 4 0 $u https://doi.org/10.1007/978-3-030-50180-8
950 $a Mathematics and Statistics (SpringerNature-11649)