New York Journal of Mathematics
Volume 21 (2015) 151-161

  

Zbigniew Blocki and Wlodzimierz Zwonek

Estimates for the Bergman kernel and the multidimensional Suita conjecture

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Published: February 26. 2015
Keywords: Suita conjecture, Bergman kernel, pluricomplex Green function, Azukawa indicatrix, convex complex elliposoid.
Subject: 32A35, 32F45, 32U35

Abstract
We study the lower bound for the Bergman kernel in terms of volume of sublevel sets of the pluricomplex Green function. We show that it implies a bound in terms of volume of the Azukawa indicatrix which can be treated as a multidimensional version of the Suita conjecture. We also prove that the corresponding upper bound holds for convex domains and discuss it in bigger detail on some convex complex ellipsoids.

Acknowledgements

The first named author was supported by the Ideas Plus grant 0001/ID3/2014/63 of the Polish Ministry Of Science and Higher Education and the second named author by the Polish National Science Centre grant 2011/03/B/ST1/04758


Author information

Zbigniew Blocki:
Uniwersytet Jagielloński, Instytut Matematyki, lojasiewicza 6, 30-348 Kraków, Poland
Zbigniew.Blocki@im.uj.edu.pl

Wlodzimierz Zwonek:
Uniwersytet Jagielloński, Instytut Matematyki, lojasiewicza 6, 30-348 Kraków, Poland
Wlodzimierz.Zwonek@im.uj.edu.pl