On the Gauss map of embedded minimal tubes
Abstract
The Gaussian image of the minimal tubes of arbitrary dimension is studied. If the angle between the flow-vector of such a surface M and its axe is equal to
then the diameter of the Gauss image of M is at least
. As a consequence we show that the length of a two dimensional minimal tube M can be estimated by the angle
and the total Gaussian curvature of M.
![𝛼(M) > 0](http://siba-ese.unile.it/plugins/generic/latexRender/cache/c976bc8575798bd52a1c147f32e2919b.png)
![2𝛼(M)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/37ab442ba7a4b21412554cb05ead316f.png)
![𝛼(M)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/1bbfee659f5cd5c6503ac9df289f562b.png)
DOI Code:
10.1285/i15900932v19n1p7
Keywords:
Minimal tubes; Gaussian map; Total gaussian curvature; Flow vector
Classification:
53A10; 53A55
Full Text: PDF