Inverse problems generated by conformal mappings on complex plane with parallel slits
P. Kargaev, E. Korotyaev
We study the properties of a conformal mapping $z(k,h)$ from $K(h)=Csmcup G_n$ where $G_n=[u_n-i|h_n|, u_n+i|h_n|], ninZ$ is a vertical slit and $h={h_n}in ell_{R}^2$, onto the complex plane with horizontal slits $g_nssR, ninZ$, with the asymptotics $z(iv,h)=iv+(iQ_0(h)+o(1))/v, v o+iy$. Here $u_{n+1}-u_ngeq 1, nin Z$, and the Dirichlet integral $Q_0(h)=iint_{C} |z'(k,h)-1|^2dudv/(2pi )0$, and the L"owner equation for $z(k,h)$ when the height of some slit $h_n$ is changed, 2) an analytic continuation of the functional $Q_0: ell_{R}^2 o R _+ $ in the domain $ {f: |Im f|
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Abstract for Sfb Preprint No. 458