Skip to main content
SpringerLink
Log in

The Hörmander Proof of the Bourgain–Milman Theorem

  • Chapter
  • First Online:
Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • 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

Institutional subscriptions

References

  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. 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. L. Hörmander, L 2 estimates and existence theorems for the \(\bar{\partial }\) operator. Acta Math. 113, 89–152 (1965)

    Google Scholar 

  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. C.-I. Hsin, The Bergman kernel on tube domains. Rev. Unión Mat. Argentina 46(1), 23–29 (2005)

    MathSciNet  MATH  Google Scholar 

  6. A. Korányi, The Bergman kernel function for tubes over convex cones. Pac. J. Math. 12(4), 1355–1359 (1962)

    Article  MATH  Google Scholar 

  7. G. Kuperberg, From the Mahler conjecture to Gauss linking integrals. Geom. Funct. Anal., 18, 870–892 (2008)

    Google Scholar 

  8. O.S. Rothaus, Domains of positivity. Abh. Math. Semin. Hamburg 24, 189–235 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  9. O.S. Rothaus, Some properties of Laplace transforms of measures. Trans. Am. Math. Soc. 131(1), 163–169 (1968)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI, 53706, USA

    Fedor Nazarov

Authors
  1. Fedor Nazarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fedor Nazarov .

Editor information

Editors and Affiliations

  1. Tel-Aviv, 69978, Israel

    Bo'az Klartag

  2. Technion Machine Learning Center, Technion, Israel Institute of Technology, Technion City, Haifa, 32000, Israel

    Shahar Mendelson

  3. Fac. Exact Sciences, School of Mathematical Sciences, University of Tel Aviv, Tel Aviv, 69978, Israel

    Vitali D. Milman

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Nazarov, F. (2012). The Hörmander Proof of the Bourgain–Milman Theorem. In: Klartag, B., Mendelson, S., Milman, V. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29849-3_20

Download citation

Publish with us

Policies and ethics

Search

Navigation