Isolated singularities of quadratic differentials arising from a module problem
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- by Jeffrey Clayton Wiener PDF
- Proc. Amer. Math. Soc. 55 (1976), 47-51 Request permission
Abstract:
If $R \subset S$ are Riemann surfaces, we will say that ${z_0} \in S - R$ is an isolated point boundary component of $R$ if there exists a neighborhood $U$ of ${z_0}$ in $S$ such that $U - \{ {z_0}\} \subset R$. We prove that the quadratic differential $Q\left ( z \right )d{z^2}$ obtained by solving the module problem $P({a_1}, \ldots ,{a_k})$ applied to a free family of homotopy classes on $R$ can be extended to ${z_0} \in S$ so that either $Q\left ( z \right )$ is regular at ${z_0}$ or $Q(z)$ has a simple pole at ${z_0}$.References
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Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 55 (1976), 47-51
- DOI: https://doi.org/10.1090/S0002-9939-1976-0393465-1
- MathSciNet review: 0393465