A Lower Bound for the Bergman Kernel and the Bourgain-milman Inequality

@inproceedings{LOCKI2013ALB,
  title={A Lower Bound for the Bergman Kernel and the Bourgain-milman Inequality},
  author={Z. B LOCKI},
  year={2013}
}
  • Z. B LOCKI
  • Published 2013
For pseudoconvex domains in C we prove a sharp lower bound for the Bergman kernel in terms of volume of sublevel sets of the pluricomplex Green function. For n = 1 it gives in particular another proof of the Suita conjecture. If Ω is convex then by Lempert’s theory the estimate takes the form KΩ(z) ≥ 1/λ2n(IΩ(z)), where IΩ(z) is the Kobayashi indicatrix at z. One can use this to simplify Nazarov’s proof of the Bourgain-Milman inequality from convex analysis. Possible further applications of… CONTINUE READING

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 18 references

La métrique de Kobayashi et la représentation des domaines sur la boule

  • L. Lempert
  • Bull. Soc. Math. France 109
  • 1981
Highly Influential
11 Excerpts

Capacities and kernels on Riemann surfaces

  • N. Suita
  • Arch. Ration. Mech. Anal. 46
  • 1972
Highly Influential
4 Excerpts

locki, Suita conjecture and the Ohsawa-Takegoshi extension theorem

  • Z B
  • Invent. Math
  • 2013
2 Excerpts

locki, Estimates for ∂̄ and optimal constants, preprint 2012, available at http://gamma.im.uj.edu.pl/ ̃blocki

  • Z B
  • 2012
1 Excerpt

The Bergman kernel on tube domains

  • C.-I. Hsin
  • Rev. Un. Mat. Argentina 46
  • 2005
1 Excerpt

Similar Papers

Loading similar papers…