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

  • B. I. Hladysh
  • O. O. Prishlyak


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.
How to Cite
Hladysh, B. I., and O. O. Prishlyak. “Deformations in the General Position of the Optimal functions on Oriented Surfaces With Boundary”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 8, Aug. 2019, pp. 1028-39,
Research articles