A priori estimates for conformal mappings on complex plane with parallel slits

Pavel Kargaev, Evgeny Korotyaev

We study the properties of a conformal mapping $z(k)$ from the plane without vertical slits $\G_n=[u_n-ih_n, u_n+ih_n], n\in\Z$ and $h=(h_n{)}_{n\in \mathbb{Z}}\in {\ell }^2$, onto the complex p…