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  3. Convex Bodies: The Brunn–Minkowski Theory
  • Cited by 164
      • 2nd edition
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 December 2013
      31 October 2013
      ISBN:
      9781139003858
      9781107601017
      DOI:
      https://doi.org/10.1017/CBO9781139003858
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.29kg, 760 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
      Series:
      Encyclopedia of Mathematics and its Applications (151)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Geometry and Topology
    Series:
    Encyclopedia of Mathematics and its Applications (151)
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    Book description

    At the heart of this monograph is the Brunn–Minkowski theory, which can be used to great effect in studying such ideas as volume and surface area and their generalizations. In particular, the notions of mixed volume and mixed area measure arise naturally and the fundamental inequalities that are satisfied by mixed volumes are considered here in detail. The author presents a comprehensive introduction to convex bodies, including full proofs for some deeper theorems. The book provides hints and pointers to connections with other fields and an exhaustive reference list. This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the Lp Brunn–Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.

    Reviews

    Review of the first edition:‘Neither one of [the old classics] may be considered a substitute for the excellent detailed monograph written by Rolf Schneider. I recommend this book to everyone who appreciates the beauty of convexity theory or who uses the strength of geometric inequalities, and to any expert who needs a reliable reference book for his/her research.'

    V. Milman Source: Bulletin of the American Mathematical Society

    Review of the first edition:‘Professor Schneider's book is the first comprehensive account of the Brunn-Minkowski theory and will immediately become the standard reference for the Aleksandrov-Fenchel inequalities and the current knowledge concerning the cases of equality and estimates of their stability. The book is aimed at a broad audience from graduate students to working professionals. The presentation is very clear and I enjoyed reading it.'

    Source: Bulletin of the London Mathematical Society

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