Teikhmyuller problem for one class of open Riemannian surfaces

V. V. Dumkin, V. G. Sheretov

A. M. Gor'kii Perm' State University

Abstract: A particular solution is given to the Teikhmyuller problem on minimizing the deviation $K[f]$ in the homotopic class $\alpha$, preserving the orientation of the quasiconformal homeomorphism $h: S_0\to S$, where $S_0$ and $S$ are open Riemannian surfaces of infinite kind. Some properties of the complex characteristic of the solution are studied.

UDC: 517.5

Received: 18.05.1969

 English version: Mathematical Notes, 1970, 7:5, 365–371

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