BOUNDS FOR CONFORMAL AUTOMOMORPHISMS OF RIEMANN SURFACES WITH CONDITION (A)
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 uppe...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2001
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172001000200002 |
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| Sumario: | 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 <FONT FACE=Symbol>³</FONT> 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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