论文标题
一个$ε$ - 由两个非重叠的大地弧形在具有恒定高斯曲率的表面上形成的顶点的特征
An $ε$-characterization of a vertex formed by two non-overlapping geodesic arcs on surfaces with constant Gaussian curvature
论文作者
论文摘要
我们确定一个正实数（重量），该数字（重量）对应于两个非重叠的测量弧的交点（顶点），该弧分别取决于两个重量，分别对应于这些GeodesIcarcs的两个点，以及一个无限的数字ε。作为限制情况，对于ε\至0，相应的权重的三合会产生了一个退化的加权费马特 - 托里切利树，它与这两个大地弧相吻合。通过将此过程应用于圆锥上的大地三角形，我们在r^3中得出了锥体点的εcharacterization。
We determine a positive real number (weight) which corresponds to the intersection point (vertex) of two non-overlapping geodesic arcs, which depends on the two weights which correspond to two points of these geodesicarcs, respectively, and an infinitesimal number ε. As a limiting case, for ε\to 0,the triad of the corresponding weights yields a degenerate weighted Fermat-Torricelli tree which coincides with these two geodesic arcs. By applying this process for a geodesic triangle on a circular cone, we derive an εcharacterization of conical points in R^3.
