  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.
