A uniqueness theorem of reflectable deformations of a Fuchsian group
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- by Jharna Sengupta PDF
- Proc. Amer. Math. Soc. 104 (1988), 1148-1152 Request permission
Abstract:
Let $\Gamma$ be a Fuchsian group of signature $(p,n,m;{\nu _1},{\nu _2}, \ldots ,{\nu _n})$; $2p - 2 + m + \sum \nolimits _{j = 1}^n {(1 - 1/{\nu _j}) > 0}$. Let ${I_1},{I_2}, \ldots ,{I_m}$ be a maximal set of inequivalent components of $\Omega \cap {\mathbf {\hat R}}$; $\Omega$ is the region of discontinuity and ${\mathbf {\hat R}}$ is the extended real line. Let $\phi$ be a quadratic differential for $\Gamma$. Let $f$ be a solution of the Schwarzian differential equation $Sf = \phi$. If $\phi$ is reflectable, $f$ maps each ${I_j}$ into a circle ${C_j}$. For each $\gamma \in \Gamma$ there is a Moebius transformation $\mathcal {X}(\gamma )$ such that $f \circ \gamma = \mathcal {X}(\gamma ) \circ f$. We prove that $\phi$ is determined by the homomorphism $\mathcal {X}$ and the circles ${C_1},{C_2}, \ldots ,{C_m}$.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1148-1152
- MSC: Primary 30F30; Secondary 20H10, 30F35, 32G15
- DOI: https://doi.org/10.1090/S0002-9939-1988-0969051-7
- MathSciNet review: 969051