Complete bounded holomorphic curves immersed in with arbitrary genus
Authors:
Francisco Martin, Masaaki Umehara and Kotaro Yamada
Journal:
Proc. Amer. Math. Soc. 137 (2009), 34373450
MSC (2000):
Primary 53A10, 32H02; Secondary 53C42, 53C50
Published electronically:
June 1, 2009
MathSciNet review:
2515413
Fulltext PDF Free Access
Abstract 
References 
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Abstract: Recently, a complete holomorphic immersion of the unit disk into whose image is bounded was constructed by the authors. In this paper, we shall prove the existence of complete holomorphic null immersions of Riemann surfaces with arbitrary genus and finite topology whose image is bounded in . As an analogue to the above construction, we also give a new method to construct complete bounded minimal immersions (resp. weakly complete maximal surfaces) with arbitrary genus and finite topology in Euclidean 3space (resp. LorentzMinkowski 3spacetime).
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Additional Information
Francisco Martin
Affiliation:
Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
Email:
fmartin@ugr.es
Masaaki Umehara
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 5600043, Japan
Email:
umehara@math.sci.osakau.ac.jp
Kotaro Yamada
Affiliation:
Faculty of Mathematics, Kyushu University, Fukuoka 8128581, Japan
Email:
kotaro@math.kyushuu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993909099535
PII:
S 00029939(09)099535
Received by editor(s):
October 26, 2008
Published electronically:
June 1, 2009
Communicated by:
Richard A. Wentworth
Article copyright:
© Copyright 2009
American Mathematical Society
