Overview
- 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
Part of the book series: Graduate Texts in Mathematics (GTM, volume 286)
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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
“The book is informative, very interesting, and mathematically accessible, and the authors have achieved the purpose that they outline above. As the title suggests, Lectures on convex geometry is well suited to be used as the prescribed textbook for graduate courses in convex geometry; this is because of its pedagogical style and the quality of the exercises. It will also be useful to students intending to pursue a research career in the area … .” (Daniel John Fresen, Mathematical Reviews, June, 2022)
Authors and Affiliations
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).
Bibliographic Information
Book Title: Lectures on Convex Geometry
Authors: Daniel Hug, Wolfgang Weil
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-50180-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-50179-2Published: 28 August 2020
Softcover ISBN: 978-3-030-50182-2Published: 28 August 2021
eBook ISBN: 978-3-030-50180-8Published: 27 August 2020
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVIII, 287
Number of Illustrations: 2 b/w illustrations, 9 illustrations in colour
Topics: Convex and Discrete Geometry, Polytopes, Measure and Integration, Functional Analysis