A Weighted Steiner Minimal Tree for Convex Quadrilaterals on the Two-Dimensional K-Plane

被引：0

作者：

Zachos, Anastasios ^{[1
]}

机构：

[1] Univ Patras, Dept Math, Rion 26500, Greece

来源：

JOURNAL OF CONVEX ANALYSIS | 2011年 / 18卷 / 01期

关键词：

Steiner minimal tree; generalized convex quadrilaterals;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a method to find a weighted Steiner minimal tree for convex quadrilaterals on a two-dimensional hemisphere of radius 1/root K, for K > 0 and the two dimensional hyperbolic plane of constant Gaussian, Curvature K, for 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.

引用

页码：139 / 152

页数：14