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.
Citation
Nedir Do Espírito-Santo. Katia Frensel. Jaime Ripoll. "On the image of the Gauss map of an immersed surface with constant mean curvature in $\mathbb{R}^{3}$." Illinois J. Math. 43 (2) 222 - 232, Summer 1999. https://doi.org/10.1215/ijm/1255985211
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