|XXXIV Workshop on Geometric Methods in Physics||28.06-4.07.2015|
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Biholomorphically invariant metrics induced by weighted Bergman kernel
In around 1947 Stefan Bergman introduced biholomorphically invariant metric by means of Bergman kernel of the domain. A little later in 1969 (around) Maciej Skwarczy\'nski introduced another biholomorphically invariant metric by means of Bergman kernel of a domain as well. It is still not clear whether these metrics are equivalent or not. In this talk we will introduce similar metrics induced by weighted Bergman kernels and try to characterize the domains of holomorphy by means of them. We will be mainly focused on weighted Skwarczy'nski distance.