Given a local diffeomorphism f : ℝn → ℝn, we consider certain in- compressibility conditions on the parallelepiped D f (x) ([0, 1]n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for f to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.
Balreira, E. C. (2010). Incompressibility and global inversion. Topological Methods in Nonlinear Analysis, 35, 69-76.
Topological Methods in Nonlinear Analysis