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A new family of Enneper type minimal surfaces


Author: Yi Fang
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
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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 [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1990-1012931-6
Article copyright: © Copyright 1990 American Mathematical Society

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