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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

HIDALGO, RUBÉN A.. BOUNDS FOR CONFORMAL AUTOMOMORPHISMS OF RIEMANN SURFACES WITH CONDITION (A). Proyecciones (Antofagasta) [online]. 2001, vol.20, n.2, pp.139-175. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172001000200002.

In this note we consider a class of groups of conformal automorphisms of closed Riemann surfaces containing those which can be lifted to some Schottky uniformization. These groups are those which satisfy a necessary condition for the Schottky lifting property. We find that all these groups have upper bound 12(g - 1), where g ³ 2 is the genus of the surface. We also describe a sequence of infinite genera g1< g2 < ... for which these upper bound is attained. Also lower bounds are found, for instance, (i ) 4(g+1) for even genus and 8(g - 1) for odd genus. Also, for cyclic groups in such a family sharp upper bounds are given

Keywords : Schottky groups; Reimann surfaces; conformal automorphisms.

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