Lectures on Convex Geometry (Graduate Texts in Mathematics, 286) - Hardcover

Hug, Daniel; Weil, Wolfgang

Hardcover

ISBN 10: 3030501795 ISBN 13: 9783030501792

Publisher: Springer, 2020

Synopsis

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 this title

About the Author

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).

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2020
• Language: English
• ISBN 10: 3030501795
• ISBN 13: 9783030501792
• Binding: Hardcover
• Number of pages: 305