Hypersurfaces of \(E_s^4\) with proper mean curvature vector (Q996132)

The compression theorem of Rubinstein and Weng say that a sufficiently small triangle on the standard sphere: of radius \(r_1\) admits a compression mapping onto an arbitrary triangle with the same side on the standard sphere of the radius \(r_2\), \(r_1 < r_2\). In the paper, this theorem is generalized for more general surfaces. Applications for Steiner's minimal tree problem and the circular billiard ball problem on surfaces are obtained.