Projection bodies

  • J. Bourgain
  • J. Lindenstrauss
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1317)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B.L.]
    J. Bourgain and J. Lindenstrauss, Nouveaux résultats sur les zonoides et les corps de projection, C.R. Acad. Sci. Paris (to appear).Google Scholar
  2. [B.L.M.]
    J. Bourgain, J. Lindenstrauss and V. Milman, Approximation of zonoids by zonotopes, Preprint IHES 1987.Google Scholar
  3. [Be.Mc]
    M. Betke and P. McMullen, Estimating the sizes of convex bodies from projections, J. Lon. Math. Soc. 27 (1983), 525–538.MathSciNetCrossRefMATHGoogle Scholar
  4. [Bol]
    E.D. Bolker, A class of convex bodies, Trans. Amer. Math. Soc. 145 (1969), 323–346.MathSciNetCrossRefMATHGoogle Scholar
  5. [Bo.F]
    T. Bonnesen and W. Fenchel, Theorie der konvexen Körper, Ergebnisse der Mathematik 3, Springer-Verlag 1934.Google Scholar
  6. [Ca]
    S. Campi, Recovering a centered convex body from the areas of its shadows, a stability estimate, Annali Di Math. (to appear).Google Scholar
  7. [C.N.S.]
    L. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for non linear second order elliptic equations 1, Monge Ampère equations, Com. Pure Appl. Math. 37 (1984).Google Scholar
  8. [C.Y.]
    S.Y. Cheng and S.T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Com. Pure Appl. Math. 29 (1976), 495–516.MathSciNetCrossRefMATHGoogle Scholar
  9. [Ch]
    G. Choquet, Lectures on analysis, Vol. III, W.A. Benjamin, Reading, Mass. 1969.Google Scholar
  10. [D1]
    V.I. Diskant, Bounds for convex surfaces with bounded curvature functions, Siberian Math. J. 12 (1971), 78–89.CrossRefMATHGoogle Scholar
  11. [D2]
    V.I. Diskant, Bounds for the discrepancy between convex bodies in terms of the isoperimetric difference, Siberian Math. J. 13 (1972), 529–532.MathSciNetCrossRefMATHGoogle Scholar
  12. [E]
    H.G. Eggleston, Convexity, Cambridge Tracts No. 47, 1958.Google Scholar
  13. [F.L.M]
    T. Figiel, J. Lindenstrauss and V. Milman, The dimension of almost spherical sections of convex bodies, Acta Math. 129 (1977), 53–94.MathSciNetCrossRefMATHGoogle Scholar
  14. [G]
    P.R. Goodey, Instability of projection bodies, Geom. Dedicata 20 (1986), 295–305.MathSciNetCrossRefMATHGoogle Scholar
  15. [Gor]
    Y. Gordon, Some inequalities for Gaussian processes and applications, Isr. J. Math. 50 (1985), 265–289.MathSciNetCrossRefMATHGoogle Scholar
  16. [J]
    F. John, Extremum problems with inequalities as subsidiary conditions, Courant anniversary volume, Interscience N.Y. 1949, 187–204.Google Scholar
  17. [K]
    H. Knothe, Contributions to the theory of convex bodies, Mich. Math. J. 4 (1957), 39–52.MathSciNetCrossRefMATHGoogle Scholar
  18. [Mü]
    C. Müller, Spherical harmonics, Springer Lecture Notes 17, 1966.Google Scholar
  19. [P]
    C.M. Petty, Projection bodies, Proc. Colloq. on Convexity, Copenhagen, 1967, 234–241.Google Scholar
  20. [Po]
    A.V. Pogorelov, The Minkowski multidimensional problem, John Wiley Publ. Washington D.C. 1978.MATHGoogle Scholar
  21. [S.W]
    R. Schneider and W. Weil, Zonoids and related topics, in Convexity and its Applications, Birkhauser Verlag 1983, 296–317.Google Scholar
  22. [Sche]
    G. Schechtman, More on emedding subspaces of L p in l pn, Compositio Math. 61 (1987), 159–170.MathSciNetGoogle Scholar
  23. [Schn1]
    R. Schneider, Zur einem Problem von Shephard über die Projektionen konvexer Körper, Math. Z. 101 (1967), 71–82.MathSciNetCrossRefMATHGoogle Scholar
  24. [Schn2]
    R. Schneider, Zur optimale Approximation konvexer Hyperflächen durch Polyeder, Math. Ann. 256 (1981), 289–301.MathSciNetCrossRefMATHGoogle Scholar
  25. [Schü]
    C. Schütt, personal communication.Google Scholar
  26. [W]
    W. Weil, Über die Projektionenkörper konvexer Polytope, Arch. Math. 22 (1971), 664–672.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. Bourgain
    • 1
    • 2
  • J. Lindenstrauss
    • 3
  1. 1.IHESFrance
  2. 2.University of IllinoisUrbana
  3. 3.Hebrew UniversityJerusalem

Personalised recommendations