Metric Projection onto Subsets of Compact Connected Two-Dimensional Riemannian Manifolds / K. S. Shklyaev. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 4. P. 15-20 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 149-153].

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}. A point x \in M^{2} is called singular if P_{E}(x) contains points from at least three distinct E_{j}. An exact estimate of the number of singular points is obtained in terms of k and the type of the manifold M^{2}. A similar estimate is proved for subsets E of a normed plane consisting of a finite number of connected components.

Key words: two-dimensional manifold, metric projection, Euler inequality, exceptional points.

№ 4/2017