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

JosÉ Antonio M. Vilhena

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

Differential Geometry 2020-01-01 v1

Authors: JosÉ Antonio M. Vilhena

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.

Keywords

minimal surface genus one catenoid end enneper end weierstrass representation elliptic functions period problem

Cite

@article{arxiv.1912.13142,
  title  = {An example of a minimal surface of genus one with two catenoid ends and one Enneper end},
  author = {JosÉ Antonio M. Vilhena},
  journal= {arXiv preprint arXiv:1912.13142},
  year   = {2020}
}

Comments

15 pages, 8 figures

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