Common maxima of distance functions on orientable Alexandrov surfaces

VÎLCU, Costin

J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 51-64 / Harvested from Project Euclid

Résumé

We find properties of the sets $M_{y}^{-1}$ of all points on a compact orientable Alexandrov surface $S$ , the distance functions of which have a common maximum at $y \in S$ . For example, the components of $M_{y}^{-1}$ 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 $M_{y}^{-1}$ , providing a relationship to the unit tangent cone at $y$ .

Détail

Publié le : 2008-01-15
Classification:  Alexandrov surface,  distance function,  53C45