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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Existence of algebraic minimal surfaces for an arbitrary puncture set
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by Katsuhiro Moriya PDF
Proc. Amer. Math. Soc. 131 (2003), 303-307 Request permission

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
  • Katsuhiro Moriya, On a variety of algebraic minimal surfaces in Euclidean $4$-space, Tokyo J. Math. 21 (1998), no. 1, 121–134. MR 1630151, DOI 10.3836/tjm/1270041990
  • —, Deformations of complete minimal surfaces of genus one with one end and finite total curvature, preprint.
  • Kichoon Yang, Complete minimal surfaces of finite total curvature, Mathematics and its Applications, vol. 294, Kluwer Academic Publishers Group, Dordrecht, 1994. MR 1325927, DOI 10.1007/978-94-017-1104-3
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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
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 303-307
  • MSC (2000): Primary 53A10
  • DOI: https://doi.org/10.1090/S0002-9939-02-06670-4
  • MathSciNet review: 1929050