Metric projection onto subsets of compact connected two-dimensional Riemannian manifoldsстатья
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Аннотация:Abstract: The paper is focused on combinatorial properties of the metric projection $P_E$ of a compact connected Riemannian two-dimensional manifold $M^2$ onto its subset $E$ consisting of $k$ closed connected sets $E_j$. The point $x \in M^2$ is called exceptional if $P_E(x)$ contains points from no less than three different $E_j$. The sharp estimate for the number of exceptional points is obtained in terms of $k$ and the type of the manifold $M^2$. Similar estimate is proved for finitely connected subsets $E$ of a normed plane.