1. On the Gauss map of embedded minimal tubes
- Author
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Reshetnikova, Irina M. and Tkachev, Vladimir G.
- Subjects
Mathematics - Differential Geometry ,Mathematics - Geometric Topology ,53A10 ,53C42 - Abstract
A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a higher-dimensional minimal tube M is controlled by the angle alpha(M) between the axis and the flow vector of M. We prove that the diameter of the Gauss image of M is at least 2alpha(M). As a consequence we derive an estimate on the length of a two-dimensional minimal tube M in terms of alpha(\M) and the total Gaussian curvature of M.
- Published
- 2009
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