In this paper we generalize the Steiner problem on planes to general regular surfaces. The main result is
Theorem 1 If A,B,C are three points on a regular surface Σ and if another point P on Σ such that the sum of the lengths of the smooth arcs Open image in new window reaches the minimum, then the angles formed by every two arcs at P are all 120°.
KeywordsConnected Graph Minimal Tree Steiner Point Unit Tangent Vector Regular Surface
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