Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture
Complex Variables
2014-05-01 v1
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.
Cite
@article{arxiv.1404.7692,
title = {Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture},
author = {Zbigniew Błocki and Włodzimierz Zwonek},
journal= {arXiv preprint arXiv:1404.7692},
year = {2014}
}
Comments
11 pages, 2 figures