Journal of Differential Geometry

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

J. Lucas M Barbosa and Manfredo P. do Carmo

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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

Permanent link to this document
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


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