Bounds for conformal automorphisms of riemann surfaces with condition (A)

• Autores: Rubén Antonio Hidalgo
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 20, Nº. 2, 2001, págs. 139-175
• Idioma: inglés
• DOI: 10.4067/S0716-09172001000200002
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• Resumen

  • 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 ≥ 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.

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