We find properties of the sets of all points on a compact orientable Alexandrov surface , the distance functions of which have a common maximum at . For example, the components of are arcwise connected and their number is at most , where is the genus of . A special attention receives the case of local tree components of , providing a relationship to the unit tangent cone at .
Costin VÎLCU. "Common maxima of distance functions on orientable Alexandrov surfaces." J. Math. Soc. Japan 60 (1) 51 - 64, January, 2008. https://doi.org/10.2969/jmsj/06010051