2019
Том 71
№ 1

All Issues

Mel’nik V. L.

Articles: 4
Brief Communications (Ukrainian)

Linearly convex domains with singularities on the boundary

Mel’nik V. L.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

Investigation of smoothness conditions on the boundary for the strong linear convexity of a domain

Mel’nik V. L.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

Topological classification of (n−1)-convex sets

Mel’nik V. L.

↓ Abstract   |   Full text (.pdf)

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.

Brief Communications (Ukrainian)

On linearly convex domains with smooth boundaries

Mel’nik V. L.

↓ Abstract   |   Full text (.pdf)

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.