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On the Gauss map of embedded minimal tubes
- Publication Year :
- 1999
- Publisher :
- Linköpings universitet, Matematik och tillämpad matematik, 1999.
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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.
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.dedup.wf.001..5d7fca9ece6078dfeb7a9d75bb9ba19a