Functions with nondegenerate critical points on the boundary of the surface

• Date: 2016
• Main Authors: Hladysh, B. I., Prishlyak, O. O., Гладиш, Б. І., Пришляк, О. О.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1819
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 restrictio...