A new family of Enneper type minimal surfaces
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- by Yi Fang PDF
- Proc. Amer. Math. Soc. 108 (1990), 993-1000 Request permission
Abstract:
An Enneper type surface is a complete immersed minimal surface in ${{\mathbf {R}}^3}$ with only one end and finite total curvature. In this paper we construct a family of Enneper type surfaces of genus 1, total curvature $- 8(2n + 1)\pi ,n = 0,1,2, \cdots$. We use the Weierstrass $\wp$ elliptic function as a tool and also prove some results about $\wp$ on a square torus.References
-
M. Abromovitz and I. Stegun, ed., Handbook of mathematical functions, Advanced Mathematics, Dover Publications, Inc., New York, 1972, chapter 18.
- Chi Cheng Chen and Fritz Gackstatter, Elliptische und hyperelliptische Funktionen und vollständige Minimalflächen vom Enneperschen Typ, Math. Ann. 259 (1982), no. 3, 359–369 (German). MR 661204, DOI 10.1007/BF01456948
- Serge Lang, Elliptic functions, 2nd ed., Graduate Texts in Mathematics, vol. 112, Springer-Verlag, New York, 1987. With an appendix by J. Tate. MR 890960, DOI 10.1007/978-1-4612-4752-4 H. B. Lawson, Jr., Lectures on minimal submanifolds. Publish or Perish Press, Berkeley, 1971.
- Robert Osserman, A survey of minimal surfaces, 2nd ed., Dover Publications, Inc., New York, 1986. MR 852409 M. Wohlgemuth, Abelsche Minimalflächen, Diplomarbeit, Universität Bonn, 1988.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 993-1000
- MSC: Primary 53A10
- DOI: https://doi.org/10.1090/S0002-9939-1990-1012931-6
- MathSciNet review: 1012931