A Weighted Steiner Minimal Tree for Convex Quadrilaterals on the Two-Dimensional K-Plane
Αναστάσιος Ζάχος · Journal of convex analysis · 2011
We provide a method to find a weighted Steiner minimal tree for convex quadrilaterals on a two-dimensional hemisphere of radius \frac{1}{\sqrt{K}} 1 K , for K>0 K > 0 and the two dimensional hyperbolic plane of constant Gaussian Curvature K, for K<0 K < 0 by introducing a method of cyclical differentiation of the objective function with respect to four variable angles. By applying this method, we find a generalized solution to a problem posed by C.F. Gauss in the spirit of weighted Steiner trees.