2008 年 60 巻 1 号 p. 51-64
We find properties of the sets My−1 of all points on a compact orientable Alexandrov surface S, the distance functions of which have a common maximum at y∈S. For example, the components of My−1 are arcwise connected and their number is at most max{1,10g−5}, where g is the genus of S. A special attention receives the case of local tree components of My−1, providing a relationship to the unit tangent cone at y.
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