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ATTACHING HANDLES TO CONSTANT-MEAN-CURVATURE-1 SURFACES IN HYPERBOLIC 3-SPACE

Published online by Cambridge University Press:  01 July 2004

Frank Pacard  and
Fernando A. A. Pimentel
Frank Pacard
Affiliation:
Laboratoire d’Analyse et de Mathématiques Appliquées, UMR 8050, Université Paris XII, Val de Marne, 61, avenue du Général de Gaulle, 94 010 CRETEIL, Cedex, France ([email protected])
Fernando A. A. Pimentel
Affiliation:
Departamento de Matematica—UFC, Av. Humberto Monte s/n, Campus do Pici, Bloco 914, CEP 60.455-760, Fontaleza—CE, Brazil ([email protected])
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Abstract

Using a connected sum construction, we prove the existence of complete non-compact embedded constant-mean-curvature-1 surfaces in hyperbolic 3-space with finitely many ends and non-trivial topology. These surfaces are obtained by desingularizing finitely many mutually tangent horospheres.

AMS 2000 Mathematics subject classification: Primary 53A10; 53A35

Keywords

constant-mean-curvature surfaceshyperbolic space
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 3 , Issue 3 , July 2004 , pp. 421 - 459
Copyright
2004 Cambridge University Press

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