A sewing theorem for quadratic differentials

Quadratic differentials on a finite Riemann surface with poles of order not exceeding two are considered. The existence of such a differential with prescribed metrical characteristics is proved. These characteristics are the following: the first coefficients in the expansions of a quadratic differential in neighborhoods of it's poles of order two, the conformal modules of the ring domains, and the heights of the strip domains in the decomposition of the Riemann surface defined by this differential. Bibl. – 5 titles.