On the retrosection theorem

Rubén A. Hidalgo

Resumen


We survey some old and new results related to the retrosection theorem and some of its extensions to compact Klein surfaces, stable Riemann surfaces and stable Klein surfaces.

Palabras clave


Riemann surfaces; Klein surfaces; Schottky Groups; superficies de Riemann; superficies de Klein; grupos de Schottky.

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Referencias


L. V. Ahlfors. Finitely generated Kleinian groups, Amer. J. Math. 86‏ (1964), 413-423; 87 (1965), 759.‏

N. L. Alling and N. Greenleaf, N. Foundations of the theory of Klein‏ surfaces. Lect. Notes in Math. 219, Springer-Verlag, (1971).‏

L. Bers. Automorphic forms for Schottky groups,. Adv. in Math. 16,‏ pp. 332-361, (1975).‏

J. Button. All Fuchsian Schottky groups are classical Schottky groups.‏ Geometry & Topology Monographs 1: The Epstein birthday schrift, pp. 117-125, (1998).

V. Chuckrow. On Schottky groups with applications to Kleinian‏ groups. Annals of Math. 88, pp. 47-61, (1968).‏

D. Hejhal. On Schottky and Teichm¨ uller spaces. Advances in Math.‏ 15, pp. 133-156, (1975).‏

B. Heltai. Symmetric Riemann surfaces, torsion subgroups and Schottky coverings. Proc. of the Amer. Math. Soc. 100, pp. 675-682, (1987).‏

L. Gerritzen and F. Herrlich. The extended Schottky space. J. Reine‏ Angew. Math. 389, pp. 190-208, (1988).‏

R. A. Hidalgo The Noded Schottky Space. Proc. London Math. Soc.‏ 3, pp. 385-403, (1996).‏

R. A. Hidalgo. Noded Fuchsian groups I. Complex variables, 36, pp. 45-66, (1998).

R. A. Hidalgo. Kleinian groups with an invariant Jordan curve: Jgroups. Pacific Journal of Math. 169, pp. 291-309, (1995).‏

R. A. Hidalgo. Schottky uniformization of stable symmetric Riemann‏ surfaces. Notas de la Sociedad Matem´ atica de Chile (NS) No. 1, pp.‏ 82-91, (2001).‏

R. A. Hidalgo. Automorphisms of Schottky type. Ann. Acad. Scie.‏ Fenn. Mathematica 30, pp. 183-204, (2005).‏

R. A. Hidalgo. Noded function groups. Complex geometry of groups‏ (Olmu´ e, 1998), 209-222, Contemp. Math., 240, Amer. Math. Soc.,‏ Providence, RI, (1999).‏

R. A. Hidalgo and B. Maskit. On Neoclassical Schottky groups. Trans.‏ of the Amer. Math. Soc. 358, pp. 4765 - 4792, (2006).‏

R. A. Hidalgo and B. Maskit. On Klein-Schottky groups. Pacific J. of‏ Math. (2) 220, pp. 313-328, (2005).‏

R. A. Hidalgo and B. Maskit. Extended Schottky groups. Preprint.‏

P. Koebe. Uber die Uniformisierung der Algebraischen Kurven II. ¨‏ Math. Ann. 69 (1910),1-81, (1910).‏

P. Koebe. Uber die Uniformisierung reeller algebraischer Kurven.‏ Nachr. Akad. Wiss. Goettingen, pp. 177-190, (1907).‏

I.Kra. Automorphic forms and Kleinian groups, Benjamin, New York,‏ (1972).‏

I. Kra. Horocyclic coordinates for Riemann surfaces and moduli spaces‏ of Kleinian groups. J. Amer. Math. Soc. 3 (1990), 499-578.‏

A. Marden. Schottky groups and circles. Contribution to Analysis, a‏ collection of papers dedicated to Lipman Bers (L.V. Ahlfors a.o., Eds.),‏ Academic Press, New York 1974, 273-278.‏

B. Maskit. Kleinian Groups. Springer-Verlag, 1988.‏

B. Maskit. On free Kleinian groups. Duke Math. J. 48 (1981), 755-765.‏

B. Maskit. A characterization of Schottky groups. J. d’Analyse Math.‏ 19 (1967), 227-230.‏

B. Maskit. On the classification of Kleinian groups:I. Koebe groups.‏ Acta Math. 135, pp. 249-270, (1975).‏

B. Maskit. On the classification of Kleinian groups:II. Signatures. Acta‏ Math. 138, pp. 17-42, (1977).‏

B. Maskit. On a class of Kleinian groups. Ann. Acad. Sci. Fenn. Ser.‏ A I Math. (1969).‏

B. Maskit. Self-maps on Kleinian groups. Amer. J. Math. XCIII, pp. 840-856, (1971).

D. Mumford. Stability of projective varieties, L’enseignement math.‏ 23, pp. 39-110, (1977).‏

S. Nag, The Complex Analytic Theory of Teichmüller Spaces (Wiley,‏ New York, (1988)).‏

H. Sato. On a paper of Zaroow. Duke Math. J. 57, pp. 205-209, (1988).‏

H. Yamamoto. An example of a nonclassical Schottky group. Duke‏ Math. J. 63, pp. 193-197, (1991).‏

R. Zarrow. Classical and nonclassical Schottky groups. Duke Math. J.‏ 42, pp. 717-724, (1975)‏




DOI: http://dx.doi.org/10.4067/S0716-09172008000100003

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