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?

We study the cycle class map from the Chow group in codimension 2 of an arithmetic scheme X (i.e., a regular proper flat scheme over an algebraic integer ring) to its new cohomology theory defined by a candidate, introduced by the second author, of the conjectural étale motivic complex with finite coefficients of Beilinson-Lichtenbaum. The injectivity of its torsion part is deduced from the fin...

If2t is replaced by 2 in (1.1) then one obtains Nehari's original injectivity criterion. Nehari's result started what is by now a considerable amount of work in this area, see, e.g. ILl . Each of the present authors has been interested in theorems of this type, expecially in generalizations to higher dimensions, lOS1,2, C1,2]. What about one dimension? For a smooth real valued function on an in...

Injectivity is an important concept in algebra, homotopy theory and elsewhere. We study the ‘injectivity consequence’ of morphisms of a category: a morphism h is a consequence of a set H of morphisms if every object injective w.r.t. all members of H is also injective w.r.t. h. We formulate a very simple logic which is always sound, i.e., whenever a proof of h from assumptions in H exists, then ...