2019
Том 71
№ 8

All Issues

Hladysh B. I.

Articles: 2
Article (Ukrainian)

Deformations in the general position of the optimal functions on oriented surfaces with boundary

Hladysh B. I., Prishlyak O. O.

↓ Abstract

Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1028-1039

UDC 516.91
It is considered simple functions with non-degenerated singularities on smooth compact oriented surfaces with the boundary. Authors describe a connection between optimality and polarity of Morse functions, $m$-functions and $mm$-functions on smooth compact oriented connected surfaces. The concept of an equipped Kronrod – Reeb graph is used to define a deformation in general position. Also, it is obtained the whole list of deformations of simple functions of one of abovedescribed class on torus, 2-dimensional disc with the boundary and on connected sum of two toruses.

Article (Ukrainian)

Functions with nondegenerate critical points on the boundary of the surface

Hladysh B. I., Prishlyak O. O.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 28-37

We prove an analog of the Morse theorem in the case where the critical point belongs to the boundary of an $n$-dimensional manifold and find the least number of critical points for the Morse functions defined on the surfaces whose critical points coincide with the critical points of their restriction to boundary.