Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 575
Estimates for conformal mappings on complex plane with parallel slits Pavel Kargaev and Evgeni Korotyaev
We study the properties of a conformal mapping $z(k)$ from $K(h)=Csmcup G_n$ where $G_n=[u_n-ih_n, u_n+ih_n], ninZ$ is a vertical slit and $h={h_n}in ell^2$, onto the complex plane with horizontal slits $g_nssR, ninZ$, with the asymptotics $z(iv)=iv+(iQ_0+o(1))/v, v oiy$. Here $u_{n+1}-u_nge 1, nin Z$, and the Dirichlet integral $Q_0=iint_{C} |z'(k)-1|^2dudv/(2pi )
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