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Zapiski Nauchnykh Seminarov POMI, 2002, Volume 286, Pages 115–125
(Mi znsl1571)
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Extremal decompositions of a Riemann surface and quasiconformal mappings of a special form. II
E. G. Emel'yanov St. Petersburg State University of Economics and Finance
Abstract:
Let $\mathfrak R$ be a finite Riemann surface. For a quadratic differential on $\mathfrak R$ associated with a certain problem on extremal decomposition of $\mathfrak R$ into $n$ domians, a parametric family of quasiconformal mappings $f_{\mathbf K}\colon\mathfrak R\to\mathfrak R_{\mathbf K}$, $\mathbf K=(k_1,\dots,k_s)$, $k_i\to\mathbb C$, is defined. These mappings map the domians of the extremal decomposition of $\mathfrak R$ onto the domians of the extremal decomposition of $\mathfrak R_{\mathbf K}$. This allows one to study the functional dependence of the problem on the parameters.
Received: 24.12.2001 Revised: 21.03.2002
Citation:
E. G. Emel'yanov, “Extremal decompositions of a Riemann surface and quasiconformal mappings of a special form. II”, Analytical theory of numbers and theory of functions. Part 18, Zap. Nauchn. Sem. POMI, 286, POMI, St. Petersburg, 2002, 115–125; J. Math. Sci. (N. Y.), 122:6 (2004), 3648–3653
Linking options:
https://www.mathnet.ru/eng/znsl1571 https://www.mathnet.ru/eng/znsl/v286/p115
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Abstract page: | 116 | Full-text PDF : | 39 |
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