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On Holomorphic Coverings of Planar Domains

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Abstract

We have previously shown that a \(p\)-fold holomorphic covering of a domain in the complex plane by another domain is extremal in the majorization principle for \(p\)-valent functions and quadratic forms associated with Green’s functions of these domains. In this paper, dual majorization principles involving both Green’s and Neumann functions are obtained, in which \(p\)-fold coverings are also extremal. The results are exemplified by applications of these principles to geometric function theory.

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Notes

  1. Similar inequalities for the Robin functions instead of Green’s functions were obtained in [8].

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Funding

This work was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2022-880) and by the Russian Foundation for Basic Research under grant 20-01-00018.

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Authors and Affiliations

  1. Far-Eastern Center of Mathematical Research, Far-Eastern Federal University, Vladivostok, 690950, Russia

    V. N. Dubinin

  2. Institute for Applied Mathematics, Far-Eastern Branch of Russian Academy of Sciences, Vladivostok, 690041, Russia

    V. N. Dubinin

Authors
  1. V. N. Dubinin
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Corresponding author

Correspondence to V. N. Dubinin.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 112, pp. 692–704 https://doi.org/10.4213/mzm13772.

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Dubinin, V.N. On Holomorphic Coverings of Planar Domains. Math Notes 112, 674–684 (2022). https://doi.org/10.1134/S0001434622110050

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  • DOI: https://doi.org/10.1134/S0001434622110050

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