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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Comparison of the Bergman kernel and the Carathéodory–Eisenman volume
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by Nikolai Nikolov and Pascal J. Thomas PDF
Proc. Amer. Math. Soc. 147 (2019), 4915-4919 Request permission


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
  • MR Author ID: 332842
  • Email:
  • Pascal J. Thomas
  • Affiliation: Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS, F-31062 Toulouse Cedex 9, France
  • MR Author ID: 238303
  • Email:
  • 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
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4915-4919
  • MSC (2010): Primary 32F45
  • DOI:
  • MathSciNet review: 4011523