Geodesic
On Holomorphic Coverings of Planar Domains
Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 692-704

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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.
Keywords: holomorphic covering, $p$-valent function, holomorphic function, Green's function, Neumann function, condenser capacity. 
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     author = {V. N. Dubinin},
     title = {On {Holomorphic} {Coverings} of {Planar} {Domains}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {692--704},
     publisher = {mathdoc},
     volume = {112},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a4/}
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V. N. Dubinin. On Holomorphic Coverings of Planar Domains. Matematičeskie zametki, Tome 112 (2022) no. 5, pp. 692-704. http://geodesic.mathdoc.fr/item/MZM_2022_112_5_a4/