Skip to main content

Volumes of sections of cubes and related problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 1376)

Keywords

  • Orthogonal Projection
  • Convex Body
  • Euclidean Ball
  • Unit Vector Basis
  • Symmetric Convex Body

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. K.M. Ball, Cube slicing in ℝn, Proc. Amer. Math. Soc. 97, 3 (1986), 465–473.

    MathSciNet  MATH  Google Scholar 

  2. K.M. Ball, Logarithmically concave functions and sections of convex sets, Studia Math. (1988), to appear.

    Google Scholar 

  3. W. Beckner, Inequalities in Fourier analysis, Ann. of Math. 102 (1975), 159–182.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Herm Jan Brascamp and Elliot H. Lieb, Best constants in Young's inequality, its converse and its generalization to more than three functions, Advances in Math. 20 (1976) 151–173.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. A. Dvoretsky and C.A. Rogers, Absolute and unconditional convergence in normed linear spaces, Proc. Nat. Acad. Sci. (U.S.A.) 36 (1950), 192–197.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. D. Hensley, Slicing the cube in ℝn and probability, Proc. Amer. Math. Soc. 73 (1979), 95–100.

    MathSciNet  MATH  Google Scholar 

  7. F. John, Extremum problems with inequalities as subsidiary conditions, Courant Anniversary Volume, Interscience, New York, 1948, 187–204.

    Google Scholar 

  8. D.R. Lewis, Ellipsoids defined by Banach ideal norms, Mathematika 26 (1979), 18–29.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. V.D. Milman and A. Pajor, Isotropic position and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in this volume.

    Google Scholar 

  10. A. Pajor, Personal communication.

    Google Scholar 

  11. M. Rogalski, Personal communication.

    Google Scholar 

  12. J.D. Vaaler, A geometric inequality with applications to linear forms, Pacific J. Math. 83 (1979), 543–553.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this chapter

Cite this chapter

Ball, K. (1989). Volumes of sections of cubes and related problems. In: Lindenstrauss, J., Milman, V.D. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090058

Download citation

  • DOI: https://doi.org/10.1007/BFb0090058

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51303-2

  • Online ISBN: 978-3-540-46189-0

  • eBook Packages: Springer Book Archive