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 Zap. Nauchn. Sem. POMI, 2000, Volume 263, Pages 157–186 (Mi znsl1140)

On extremal decomposition problem in the family of general type systems of domains

G. V. Kuz'mina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We prove a theorem extending results of the theory of extremal decomposition problems to families of systems of domains of general type. The considered families of systems of domains contain domains similar in the small to end and strip domains of a quadratic differential having poles of arbitrary orders $n_k\ge3$ at some marked points $c_k$, $k=1,…,p$. In this case, we give a simple definition of reduced modules for the considered systems of domains. Some other definitions for the treated systems of domains are also considered. Some examples are given illustrating the possibilities of applications of the theorem obtained in the problems on extremal decomposition.

Full text: PDF file (297 kB)

English version:
Journal of Mathematical Sciences (New York), 2002, 110:6, 3121–3139

Bibliographic databases:

UDC: 517.54

Citation: G. V. Kuz'mina, “On extremal decomposition problem in the family of general type systems of domains”, Analytical theory of numbers and theory of functions. Part 16, Zap. Nauchn. Sem. POMI, 263, POMI, St. Petersburg, 2000, 157–186; J. Math. Sci. (New York), 110:6 (2002), 3121–3139

Citation in format AMSBIB
\Bibitem{Kuz00} \by G.~V.~Kuz'mina \paper On extremal decomposition problem in the family of general type systems of domains \inbook Analytical theory of numbers and theory of functions. Part~16 \serial Zap. Nauchn. Sem. POMI \yr 2000 \vol 263 \pages 157--186 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl1140} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1756344} \zmath{https://zbmath.org/?q=an:1008.30015} \transl \jour J. Math. Sci. (New York) \yr 2002 \vol 110 \issue 6 \pages 3121--3139 \crossref{https://doi.org/10.1023/A:1015476429123} 

• http://mi.mathnet.ru/eng/znsl1140
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This publication is cited in the following articles:
1. V. N. Dubinin, N. V. Eirikh, “Obobschennyi privedennyi modul”, Dalnevost. matem. zhurn., 3:2 (2002), 150–164