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.
Incompressibility and Global InversionTopological Methods in Nonlinear Analysis
Citation InformationBalreira, E. C. (2010). Incompressibility and global inversion. Topological Methods in Nonlinear Analysis, 35, 69-76.