Lectures on Convex Geometry

Released on by Daniel Hug
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  • Lectures on Convex Geometry Book Detail

  • Author : Daniel Hug
  • Release Date : 2020-08-27
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 287
  • ISBN 13 : 3030501809
  • File Size : 74,74 MB
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Lectures on Convex Geometry by Daniel Hug PDF Summary

Book Description: 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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