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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 $3$-space as a branched complete minimal surface of finite total curvature called an algebraic minimal surface.

References [Enhancements On Off] (What's this?)

  • 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,
  • 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

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Additional Information

Katsuhiro Moriya
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

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