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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  -space as a branched complete minimal surface of finite total curvature called an algebraic minimal surface.
- 1.
Katsuhiro
Moriya, On a variety of algebraic minimal surfaces in Euclidean
4-space, Tokyo J. Math. 21 (1998), no. 1,
121–134. MR 1630151
(99h:53010), http://dx.doi.org/10.3836/tjm/1270041990
- 2.
-, Deformations of complete minimal surfaces of genus one with one end and finite total curvature, preprint.
- 3.
Kichoon
Yang, Complete minimal surfaces of finite total curvature,
Mathematics and its Applications, vol. 294, Kluwer Academic Publishers
Group, Dordrecht, 1994. MR 1325927
(96d:53009)
- 1.
- K. Moriya, On a variety of algebraic minimal surfaces in Euclidean
 -space, Tokyo J. Math. 21 (1998), no. 1, 121-134. MR 99h:53010
- 2.
- -, Deformations of complete minimal surfaces of genus one with one end and finite total curvature, preprint.
- 3.
- K. Yang, Complete minimal surfaces of finite total curvature, Kluwer Academic Publishers Group, Dordrecht, 1994. MR 96d:53009
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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
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