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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation