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

  title={A Lower Bound for the Bergman Kernel and the Bourgain-milman Inequality},
  author={Z. B LOCKI},
  • 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

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