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Sfb288 logo 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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