2019
Том 71
№ 11

All Issues

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

Hladysh B. I., Prishlyak O. O.


Abstract

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.

Citation Example: Hladysh B. I., Prishlyak O. O. Deformations in the general position of the optimal functions on oriented surfaces with boundary // Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1028-1039.