A uniqueness theorem of reflectable deformations of a Fuchsian group
Proc. Amer. Math. Soc. 104 (1988), 1148-1152
Primary 30F30; Secondary 20H10, 30F35, 32G15
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Abstract: Let be a Fuchsian group of signature ; . Let be a maximal set of inequivalent components of ; is the region of discontinuity and is the extended real line. Let be a quadratic differential for . Let be a solution of the Schwarzian differential equation . If is reflectable, maps each into a circle . For each there is a Moebius transformation such that . We prove that is determined by the homomorphism and the circles .
M. Gallo and R.
Michael Porter, Projective structures on open surfaces,
Kleinian groups and related topics (Oaxtepec, 1981) Lecture Notes in
Math., vol. 971, Springer, Berlin-New York, 1983,
pp. 36–47. MR 690277
-, Extended monodromy mapping for bordered Riemann surfaces (to appear).
Kra, Deformations of Fuchsian groups. II, Duke Math. J.
38 (1971), 499–508. MR 0285734
Kra, A generalization of a theorem of
Poincaré, Proc. Amer. Math. Soc. 27 (1971), 299–302.
0301189 (46 #347), http://dx.doi.org/10.1090/S0002-9939-1971-0301189-7
Kra, Automorphic forms and Kleinian groups, W. A. Benjamin,
Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0357775
- D. M. Gallo and R. M. Porter, Projective structures on open Riemann surfaces, Lecture Notes in Math., vol. 971, Springer-Verlag, Berlin and New York, 1981, pp. 36-47. MR 690277 (84f:30054)
- -, Extended monodromy mapping for bordered Riemann surfaces (to appear).
- I. Kra, Deformation of Fuchsian groups. II, Duke Math. J. 38 (1971), 499-508. MR 0285734 (44:2951)
- -, A generalization of a Theorem of Poincaré, Proc. Amer. Math. Soc. 27 (1971), 299-302. MR 0301189 (46:347)
- -, Automorphic forms and Kleinian groups, Benjamin, Reading, Mass., 1972. MR 0357775 (50:10242)
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