Circular m-functions - Kurashvili, T. A. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
Circular m-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifol dM^4 with boundary ∂M^4 that satisfies the condition ξ(∂M 4) = ξ(M^4,∂M^4) = 0 but does not contain any circularm-function. We prove that a manifold with boundary M^n (n ≥ 5) such that ξ(∂M^n , ∂M^n ) = 0 always contains a circularm-function without critical points in the interior manifold.