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 Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 699–707 (Mi izv1787)

Extremal properties of mappings onto surfaces with parallel slits

Yu. E. Alenitsyn

Abstract: In the present paper an are a theorem is established for certain regular functions associated with multivalent mappings of a finitely connected domain onto a surface with parallel slits. Several consequences of this theorem generalize well-known results from the theory of univalent conformal mappings. The notion of the generalized span of a domain is introduced. It is then shown that it possesses certain properties completely analogous to the basic extremal properties of the span of a domain. Grötzsch's theorem concerning the range of the first coefficient of the regular part of the normalized Laurent expansion of a univalent function about a pole is extended to multivalent functions.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 1–8

Bibliographic databases:

UDC: 517.5
MSC: Primary 30C75; Secondary 30C25, 30C40

Citation: Yu. E. Alenitsyn, “Extremal properties of mappings onto surfaces with parallel slits”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 699–707; Math. USSR-Izv., 13:1 (1979), 1–8

Citation in format AMSBIB
\Bibitem{Ale78} \by Yu.~E.~Alenitsyn \paper Extremal properties of mappings onto surfaces with parallel slits \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1978 \vol 42 \issue 4 \pages 699--707 \mathnet{http://mi.mathnet.ru/izv1787} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=508822} \zmath{https://zbmath.org/?q=an:0425.30013|0386.30010} \transl \jour Math. USSR-Izv. \yr 1979 \vol 13 \issue 1 \pages 1--8 \crossref{https://doi.org/10.1070/IM1979v013n01ABEH002008} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17800001}