Skip to content

Your Cart


You have 0 items in your cart.

Register Sign in Wishlist

Convex Bodies: The Brunn–Minkowski Theory

2nd Edition

$165.00 (C)

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: December 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107601017

$ 165.00 (C)

Add to cart Add to wishlist

Other available formats:

Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • 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.

    • Extensively revised to reflect developments in the field since the publication of the first edition in 1993
    • Comprehensive coverage serves newcomers in the field as well as experienced researchers
    • Introductory material has been tried and tested for classroom use
    Read more

    Reviews & endorsements

    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, 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.' Bulletin of the London Mathematical Society

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Edition: 2nd Edition
    • Date Published: December 2013
    • format: Hardback
    • isbn: 9781107601017
    • length: 760 pages
    • dimensions: 236 x 163 x 46 mm
    • weight: 1.29kg
    • availability: Available
  • Table of Contents

    Preface to the second edition
    Preface to the first edition
    General hints to the literature
    Conventions and notation
    1. Basic convexity
    2. Boundary structure
    3. Minkowski addition
    4. Support measures and intrinsic volumes
    5. Mixed volumes and related concepts
    6. Valuations on convex bodies
    7. Inequalities for mixed volumes
    8. Determination by area measures and curvatures
    9. Extensions and analogues of the Brunn–Minkowski theory
    10. Affine constructions and inequalities
    Appendix. Spherical harmonics
    Notation index
    Author index
    Subject index.

  • Resources for

    Convex Bodies: The Brunn–Minkowski Theory

    Rolf Schneider

    General Resources

    Welcome to the resources site

    Here you will find free-of-charge online materials to accompany this book. The range of materials we provide across our academic and higher education titles are an integral part of the book package whether you are a student, instructor, researcher or professional.

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    *This title has one or more locked files and access is given only to instructors adopting the textbook for their class. We need to enforce this strictly so that solutions are not made available to students. To gain access to locked resources you either need first to sign in or register for an account.

    These resources are provided free of charge by Cambridge University Press with permission of the author of the corresponding work, but are subject to copyright. You are permitted to view, print and download these resources for your own personal use only, provided any copyright lines on the resources are not removed or altered in any way. Any other use, including but not limited to distribution of the resources in modified form, or via electronic or other media, is strictly prohibited unless you have permission from the author of the corresponding work and provided you give appropriate acknowledgement of the source.

    If you are having problems accessing these resources please email

  • Author

    Rolf Schneider, Albert-Ludwigs-Universität Freiburg, Germany
    Rolf Schneider is Professor Emeritus in the Faculty of Mathematics and Physics at Albert-Ludwigs-Universität Freiburg, Germany.

related journals

Sign In

Please sign in to access your account


Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.