On the image of the Gauss map of an immersed surface with constant mean curvature in $\mathbb{R}^{3}$
Do Espírito-Santo, Nedir ; Frensel, Katia ; Ripoll, Jaime
Illinois J. Math., Tome 43 (1999) no. 3, p. 222-232 / Harvested from Project Euclid
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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.
Publié le : 1999-06-15
Classification:  53A10,  53C42 
@article{1255985211,
     author = {Do Esp\'\i rito-Santo, Nedir and Frensel, Katia and Ripoll, Jaime},
     title = {On the image of the Gauss map of an immersed surface with constant mean curvature in $\mathbb{R}^{3}$},
     journal = {Illinois J. Math.},
     volume = {43},
     number = {3},
     year = {1999},
     pages = { 222-232},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255985211}
}

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., Tome 43 (1999) no. 3, pp.  222-232. http://gdmltest.u-ga.fr/item/1255985211/