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Comparison of the Bergman kernel and the Carathéodory-Eisenman volume


Authors: Nikolai Nikolov and Pascal J. Thomas
Journal: Proc. Amer. Math. Soc. 147 (2019), 4915-4919
MSC (2010): Primary 32F45
DOI: https://doi.org/10.1090/proc/14604
Published electronically: May 29, 2019
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Abstract: It is proved that for any domain in $ \mathbb{C}^n$ the Carathéodory-Eisenman volume is comparable with the volume of the indicatrix of the Carathéodory metric up to small/large constants depending only on $ n.$ Then the ``multi-dimensional Suita conjecture'' theorem of Błocki and Zwonek implies a comparable relationship between these volumes and the Bergman kernel.


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Additional Information

Nikolai Nikolov
Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev 8, 1113 Sofia, Bulgaria – and – Faculty of Information Sciences, State University of Library Studies and Information Technologies, Shipchenski prohod 69A, 1574 Sofia, Bulgaria
Email: nik@math.bas.bg

Pascal J. Thomas
Affiliation: Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS, F-31062 Toulouse Cedex 9, France
Email: pascal.thomas@math.univ-toulouse.fr

DOI: https://doi.org/10.1090/proc/14604
Keywords: Bergman kernel, Azukawa metric, Carath\'eodory metric, Carath\'eodory--Eisenman volume
Received by editor(s): December 18, 2018
Received by editor(s) in revised form: February 26, 2019
Published electronically: May 29, 2019
Additional Notes: The first named author was partially supported by the Bulgarian National Science Fund, Ministry of Education and Science of Bulgaria under contract DN 12/2. This paper was started while the first author was visiting the Paul Sabatier University, Toulouse, in November 2018 as a guest professor.
Communicated by: Harold P. Boas
Article copyright: © Copyright 2019 American Mathematical Society