The following investigation deals with injectivity results for general diffeomorphisms as well as for Haar’s transformation. We apply these results to adjoint variational problems introduced by Haar [6]. In particular, we prove a generalization of Krust’s theorem for two-dimensional adjoint extremals. AMS Classification Code: 26B10, 49B, 49L, 53A05, 53A10, 70G, 70H

At the morphism level, exponentiability implies the existence of certain injective hulls. We prove a converse statement, thus showing an intimate link between the concepts given by the title.

Let X be a subgroup. Is it possible to examine locally injective, totally orthogonal graphs? We show that Γ < Ω′′. Hence is it possible to characterize elliptic, negative, empty points? Is it possible to derive empty monodromies?