Geodesic
Keldysh--Sedov formulas and differentiability with respect to the parameter of families of univalent functions in $n$-connected domains
Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 878-889.

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We introduce families of functions $F_j(w,t)$ mapping $(n+1)$-connected domains onto circular domains in the $z$-plane. Denote by $\Phi_j(z,t)$ the families of functions inverse to $F_j(w,t)$. Theorems 1-?4 treat differentiability properties of these families with respect to $t$ at a point $t=t_0$. We present formulas for the first derivative with respect to $t$. Corollaries of the theorems obtained are given. As a particular case, we deduce the theorem due to Kufarev for the disk and the theorem of Kufarev and Genina (Semukhina) for the annulus. 
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     title = {Keldysh--Sedov formulas and differentiability with respect to the parameter of families of univalent functions in $n$-connected domains},
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A. S. Sorokin. Keldysh--Sedov formulas and differentiability with respect to the parameter of families of univalent functions in $n$-connected domains. Matematičeskie zametki, Tome 58 (1995) no. 6, pp. 878-889. http://geodesic.mathdoc.fr/item/MZM_1995_58_6_a7/

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