Geodesic
A Weighted Steiner Minimal Tree for Convex Quadrilaterals on the Two-Dimensional K-Plane
Journal of convex analysis, Tome 18 (2011) no. 1, pp. 139-152

Voir la notice de l'article provenant de la source Heldermann Verlag

We provide a method to find a weighted Steiner minimal tree for convex quadrilaterals on a two-dimensional hemisphere of radius $\frac{1}{\sqrt{K}}$, for $K>0$ and the two dimensional hyperbolic plane of constant Gaussian Curvature K, for $K0$ 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.
Classification : 51E12, 52A10, 52A55, 51E10
Mots-clés : Steiner minimal tree, generalized convex quadrilaterals 
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     author = {A. Zachos},
     title = {A {Weighted} {Steiner} {Minimal} {Tree} for {Convex} {Quadrilaterals} on the {Two-Dimensional} {K-Plane}},
     journal = {Journal of convex analysis},
     pages = {139--152},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a6/}
}
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A. Zachos. A Weighted Steiner Minimal Tree for Convex Quadrilaterals on the Two-Dimensional K-Plane. Journal of convex analysis, Tome 18 (2011) no. 1, pp. 139-152. http://geodesic.mathdoc.fr/item/JCA_2011_18_1_JCA_2011_18_1_a6/