Advertisement

The Hörmander Proof of the Bourgain–Milman Theorem

  • Fedor NazarovEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2050)

Abstract

We give a proof of the Bourgain–Milman theorem based on Hörmander’s Existence Theorem for solutions of the \(\bar{\partial }\)-problem.

Keywords

Paley-Wiener Space Origin-symmetric Convex Body Bergman Space Standard Conformal Mapping Tube Domain 
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.

References

  1. 1.
    K. Ball, in Flavors of Geometry, ed. by S. Levy. Math. Sci. Res. Inst. Publ., vol. 31 (Cambridge University Press, Cambridge, 1997)Google Scholar
  2. 2.
    J. Bourgain, V.D. Milman, New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^{n}\). Invent. Math. 88(2), 319–340 (1987)Google Scholar
  3. 3.
    L. Hörmander, L 2 estimates and existence theorems for the \(\bar{\partial }\) operator. Acta Math. 113, 89–152 (1965)Google Scholar
  4. 4.
    L. Hörmander, A history of existence theorems for the Cauchy-Riemann complex in L 2 spaces. J. Geom. Anal. 13(2), 329–357 (2003)Google Scholar
  5. 5.
    C.-I. Hsin, The Bergman kernel on tube domains. Rev. Unión Mat. Argentina 46(1), 23–29 (2005)MathSciNetzbMATHGoogle Scholar
  6. 6.
    A. Korányi, The Bergman kernel function for tubes over convex cones. Pac. J. Math. 12(4), 1355–1359 (1962)zbMATHCrossRefGoogle Scholar
  7. 7.
    G. Kuperberg, From the Mahler conjecture to Gauss linking integrals. Geom. Funct. Anal., 18, 870–892 (2008)Google Scholar
  8. 8.
    O.S. Rothaus, Domains of positivity. Abh. Math. Semin. Hamburg 24, 189–235 (1960)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    O.S. Rothaus, Some properties of Laplace transforms of measures. Trans. Am. Math. Soc. 131(1), 163–169 (1968)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations