We establish a relationship between geodesic nets and critical points of the distance function. We bound the number of balanced points for certain minimizing geodesic nets on manifolds homeomorphic to the n-sphere. This result is used to give conditions under which a minimizing geodesic flower degenerates into a simple closed geodesic.

中文翻译：

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最小化测地网和距离的临界点

我们建立了测地线网与距离函数的临界点之间的关系。我们对同胚于n球面的流形上的某些最小化测地线网限制了平衡点的数量。该结果用于给出最小化测地线花退化为简单闭合测地线的条件。