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
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