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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Existence of algebraic minimal surfaces for an arbitrary puncture set


Author: Katsuhiro Moriya
Journal: Proc. Amer. Math. Soc. 131 (2003), 303-307
MSC (2000): Primary 53A10
Published electronically: June 12, 2002
MathSciNet review: 1929050
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Abstract: We will show that any punctured Riemann surface can be conformally immersed into a Euclidean $3$-space as a branched complete minimal surface of finite total curvature called an algebraic minimal surface.


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Additional Information

Katsuhiro Moriya
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan
Email: moriya@math.tsukuba.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06670-4
PII: S 0002-9939(02)06670-4
Keywords: Minimal surface, Riemann surface, puncture set
Received by editor(s): February 17, 2000
Received by editor(s) in revised form: August 16, 2001
Published electronically: June 12, 2002
Communicated by: Bennett Chow
Article copyright: © Copyright 2002 American Mathematical Society