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arXiv · 1912.13142

An example of a minimal surface of genus one with two catenoid ends and one Enneper end

JosÉ Antonio M. Vilhena
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Abstract

In this paper we construct an example of a complete immersed minimal surface in $\mathbb{R}^3$ of genus one with two embedded catenoid-type ends, one Enneper-type end and total Gauss curvature $-16\pi.$ The proof of the existence of this example, was obtained using the Weierstrass representation, the theory of elliptic functions and explicitly solving the period problem.

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JosÉ Antonio M. Vilhena. 2019-12-31. An example of a minimal surface of genus one with two catenoid ends and one Enneper end. https://arxiv.org/abs/1912.13142

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