On the Gauss map of embedded minimal tubes

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dc.creatorReshetnikova, Irina M.
dc.creatorTkachev, Vladimir G.
dc.date2009-03-02
dc.date.accessioned2026-07-07T12:48:06Z
dc.date.available2026-07-07T12:48:06Z
dc.descriptionA 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.
dc.identifierhttps://arxiv.org/abs/0903.0228
dc.identifierhttp://arxiv.org/abs/0903.0228
dc.identifierNote di Matematica, 19(1999), no. 1, 7-17
dc.identifierdoi:10.1285/i15900932v19n1p7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221942
dc.subjectDifferential Geometry
dc.subjectGeometric Topology
dc.subject53A10; 53C42
dc.titleOn the Gauss map of embedded minimal tubes
dc.typetext

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