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Lectures on convex geometry

Hug, Daniel.

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Lectures on convex geometry

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on convex geometry/ by Daniel Hug, Wolfgang Weil.
作者:	Hug, Daniel.
其他作者:	Weil, Wolfgang.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xviii, 287 p. :ill., digital ;24 cm.
內容註:	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
標題:	Convex geometry. -
電子資源:	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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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.
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