BOUNDS FOR CONFORMAL
AUTOMOMORPHISMS OF RIEMANN
SURFACES WITH CONDITION (A) *

RUBÉN A. HIDALGO
Universidad Técnica Federico Santa María, Chile

Abstract

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.

Subjclass : [2000] Primary 30F10, 30F40
Keywords : Schottky groups, Reimann surfaces, conformal automorphisms

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Received : May, 2000.

RUBEN A. HIDALGO
Departamento de Matemática
Universidad Técnica Federico Santa María
Casilla 110-V
Valparaíso
Chile
E-MAIL: rhidalgo@mat.utfsm.cl