2022/07/20 by Rustam Sadykov, Sadykov, Rustam, Trunov, Stanislav
Mathematics · #Geometric Analysis and Curvature Flows #History and Theory of Mathematics #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2207.10072
Introduced by Seifert and Threlfall, cylindrical neighborhoods is an essential tool in the Lusternik-Schnirelmann theory. We conjecture that every isolated critical point of a smooth function admits a cylindrical ball neighborhood. We show that the conjecture is true for cone-like critical points, Cornea reasonable critical points, and critical points that satisfy the Rothe H hypothesis. In particular, the conjecture holds true at least for those critical points that are not infinitely degenerate.