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Mat. Sb., 2015, Volume 206, Number 1, Pages 175–190 (Mi msb8326)  

This article is cited in 1 scientific paper (total in 1 paper)

Carathéodory domains and Rudin's converse of the maximum modulus principle

K. Yu. Fedorovskiyab

a N. E. Bauman Moscow State Technical University
b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We obtain extensions of the classical Rudin theorem on the converse of the maximum modulus principle from the unit disc to Carathéodory domains. The proofs are based on recent results about properties of conformal mappings of Carathéodory domains, which are also considered in the paper.
Bibliography: 18 titles.

Keywords: Carathéodory domain, maximum modulus principle, meromorphic functions, equality in the sense of conformal mappings.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00434
13-01-12430
Ministry of Education and Science of the Russian Federation НШ-2900.2014.1
1.2640.2014
Dynasty Foundation
The author was partially supported by the Russian Foundation for Basic Research (grant nos. 12-01-00434 and 13-01-12430), the Programme for the Support of Leading Scientific Schools of the Russian Federation (grant НШ-2900.2014.1), the Russian Ministry of Education and Science (project no. 1.2640.2014), and by Dmitry Zimin's "Dynasty" Foundation.


DOI: https://doi.org/10.4213/sm8326

Full text: PDF file (530 kB)
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English version:
Sbornik: Mathematics, 2015, 206:1, 161–174

Bibliographic databases:

UDC: 517.542+517.547.5
MSC: 30C80
Received: 14.01.2014 and 24.10.2014

Citation: K. Yu. Fedorovskiy, “Carathéodory domains and Rudin's converse of the maximum modulus principle”, Mat. Sb., 206:1 (2015), 175–190; Sb. Math., 206:1 (2015), 161–174

Citation in format AMSBIB
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\pages 161--174
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. Yu. Fedorovskiy, “Carathéodory sets and analytic balayage of measures”, Sb. Math., 209:9 (2018), 1376–1389  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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