1. On Holomorphic Coverings of Planar Domains.
- Author
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Dubinin, V. N.
- Subjects
- *
GREEN'S functions , *GEOMETRIC function theory , *QUADRATIC forms , *QUADRATIC differentials , *HOLOMORPHIC functions - Abstract
We have previously shown that a -fold holomorphic covering of a domain in the complex plane by another domain is extremal in the majorization principle for -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 -fold coverings are also extremal. The results are exemplified by applications of these principles to geometric function theory. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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