A characteristic property of Delaunay surfaces

Thomas Hasanis; Rafael López

A characteristic property of Delaunay surfaces

Differential Geometry 2019-12-18 v1

Authors: Thomas Hasanis , Rafael López

Abstract

We prove that Delaunay surfaces, except the plane and the catenoid, are the only surfaces in Euclidean space with nonzero constant mean curvature that can be expressed as an implicit equation of type $f(x)+g(y)+h(z)=0$ , where $f$ , $g$ and $h$ are smooth real functions of one variable.

Keywords

delaunay surfaces constant mean curvature implicit equation euclidean space catenoid characteristic property

Cite

@article{arxiv.1912.07867,
  title  = {A characteristic property of Delaunay surfaces},
  author = {Thomas Hasanis and Rafael López},
  journal= {arXiv preprint arXiv:1912.07867},
  year   = {2019}
}

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