Advertisement

Projection bodies

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

Keywords

Banach Space Convex Body Euclidean Ball Symmetric Convex Body Projection 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [Bol]
    E.D. Bolker, A class of convex bodies, Trans. Amer. Math. Soc. 145 (1969), 323–346.MathSciNetCrossRefzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle 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.CrossRefzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [G]
    P.R. Goodey, Instability of projection bodies, Geom. Dedicata 20 (1986), 295–305.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [Gor]
    Y. Gordon, Some inequalities for Gaussian processes and applications, Isr. J. Math. 50 (1985), 265–289.MathSciNetCrossRefzbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle 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.zbMATHGoogle 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.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [Schn2]
    R. Schneider, Zur optimale Approximation konvexer Hyperflächen durch Polyeder, Math. Ann. 256 (1981), 289–301.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [Schü]
    C. Schütt, personal communication.Google Scholar
  26. [W]
    W. Weil, Über die Projektionenkörper konvexer Polytope, Arch. Math. 22 (1971), 664–672.MathSciNetCrossRefzbMATHGoogle 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