3 research outputs found
On the Gauss map of embedded minimal tubes
Full text linkA 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
