## Journal of Differential Geometry

### On regular algebraic surfaces of $\mathbb{R}^3$ with constant mean curvature

#### Abstract

We consider regular surfaces $M$ that are given as the zeros of a polynomial function $p : \mathbb{R}^3 \to \mathbb{R}$, where the gradient of $p$ vanishes nowhere. We assume that $M$ has non-zero constant mean curvature and prove that there exist only two examples of such surfaces, namely the sphere and the circular cylinder.

#### Article information

Source
J. Differential Geom., Volume 102, Number 2 (2016), 173-178.

Dates
First available in Project Euclid: 27 January 2016

https://projecteuclid.org/euclid.jdg/1453910452

Digital Object Identifier
doi:10.4310/jdg/1453910452

Mathematical Reviews number (MathSciNet)
MR3454544

Zentralblatt MATH identifier
1344.53009

#### Citation

Barbosa, J. Lucas M; do Carmo, Manfredo P. On regular algebraic surfaces of $\mathbb{R}^3$ with constant mean curvature. J. Differential Geom. 102 (2016), no. 2, 173--178. doi:10.4310/jdg/1453910452. https://projecteuclid.org/euclid.jdg/1453910452