Mel’nik V. L.
Ukr. Mat. Zh. - 2000. - 52, № 3. - pp. 403-408
We present a topological classification of linearly convex domains with almost smooth boundary whose singularities lie in a hyperplane. We investigate sets with linearly convex boundary and the closures of linearly convex domains.
Ukr. Mat. Zh. - 1999. - 51, № 12. - pp. 1710–1713
We construct a counterexample for the hypothesis that the strong linear convexity of a domain follows from the linear convexity if the set of singularities does not split the boundary.
Ukr. Mat. Zh. - 1998. - 50, № 9. - pp. 1236–1243
We investigate the properties of (n−1)-convex sets associated with the properties of conjugate sets. We give a complete topological classification of (n−1)-convex sets.
Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1553–1556
We establish that an arbitrary locally linearly convex domain with a smooth boundary is strongly linearly convex.