Estimates for the Bergman Kernel and the Multidimensional Suita Conjecture

2014/04/30 by Zbigniew B Locki, Błocki, Zbigniew, W Lodzimierz Zwonek +1
Mathematics · #30C85 #32A25 #32U35 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1404.7692

openalex publication_date 2014/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

Citations

• A solution of an L² extension problem with optimal estimate and applications

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