A sewing theorem for quadratic differentials |
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Authors: | E G Emel’yanov |
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Institution: | (1) Departamento de Matemática, Universidad Técnica Federico Santa María Casilla, 110-V Valparaíso, Chile |
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Abstract: | Quadratic differentials
\mathfrakQ(z)dz2 \mathfrak{Q}(z)d{z^2} on a finite Riemann surface with poles of order not exceeding two are considered. The existence of such a differential with
prescribed metric characteristics is proved. These characteristics are the following: the leading coefficients in the expansions
of the function
\mathfrakQ(z) \mathfrak{Q}(z) in neighborhoods of its 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 the structure of trajectories of this differential. Bibliography: 5
titles. |
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Keywords: | |
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