Geodesic
Extremal decompositions of a Riemann surface and quasiconformal mappings of a special form. II
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 115-125 
E. G. Emel'yanov. Extremal decompositions of a Riemann surface and quasiconformal mappings of a special form. II. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 18, Tome 286 (2002), pp. 115-125. http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a8/
@article{ZNSL_2002_286_a8,
     author = {E. G. Emel'yanov},
     title = {Extremal decompositions of a {Riemann} surface and quasiconformal mappings of a special {form.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {115--125},
     year = {2002},
     volume = {286},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_286_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.