## Illinois Journal of Mathematics

### On the image of the Gauss map of an immersed surface with constant mean curvature in $\mathbb{R}^{3}$

#### Abstract

We prove, generalizing a well known property of Delaunay surfaces, that if the Gauss image of a cmc surface in the Euclidean space is a compact surface with boundary, then any connected component of sphere minus the image is a strictly convex domain. We also obtain conditions under which the Gauss image has a regular boundary. These results relate to the question, raised by do Carmo, of whether the Gauss image of a complete cmc surface contains an equator of the sphere.

#### Article information

Source
Illinois J. Math., Volume 43, Issue 2 (1999), 222-232.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.ijm/1255985211

Digital Object Identifier
doi:10.1215/ijm/1255985211

Mathematical Reviews number (MathSciNet)
MR1703184

Zentralblatt MATH identifier
0958.53009

#### Citation

Do Espírito-Santo, Nedir; Frensel, Katia; Ripoll, Jaime. On the image of the Gauss map of an immersed surface with constant mean curvature in $\mathbb{R}^{3}$. Illinois J. Math. 43 (1999), no. 2, 222--232. doi:10.1215/ijm/1255985211. https://projecteuclid.org/euclid.ijm/1255985211