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Graduate Texts in Mathematics

Lectures on Convex Geometry

Authors: Hug, Daniel, Weil, Wolfgang

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  • The text provides a self-contained and efficient one-semester introduction to the main concepts and results in convex geometry.
  • The selected topics highlight the interactions between geometry and analysis, treating several topics for the first time in an introductory textbook.
  • Suggestions for further reading and a large number of solved exercises complement the main text
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  • ISBN 978-3-030-50180-8
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About this Textbook

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.


About the authors

Prof. Dr. Daniel Hug (1965–) obtained his Ph.D. in Mathematics (1994) and Habilitation (2000) at Univ. Freiburg. He was an assistant Professor at TU Vienna (2000), trained and acted as a High School Teacher (2005–2007), was Professor in Duisburg-Essen (2007), Associate Professor in Karlsruhe (2007–2011), and has been a Professor in Karlsruhe since 2011.

Prof. Dr. Wolfgang Weil (1945–2018) obtained his Ph.D. in Mathematics at Univ. Frankfurt/Main in 1971 and his Habilitation in Freiburg (1976). He was an Assistant Professor in Berlin and Freiburg, Akad. Rat in Freiburg (1978–1980), and was a Professor in Karlsruhe from 1980. He was a Guest Professor in Norman, Oklahoma, USA (1985 and 1990).

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $59.99
price for Mexico
  • ISBN 978-3-030-50180-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $74.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Convex Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
286
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-50180-8
DOI
10.1007/978-3-030-50180-8
Hardcover ISBN
978-3-030-50179-2
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVIII, 287
Number of Illustrations
2 b/w illustrations, 9 illustrations in colour
Topics

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