Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Incompressibility And Global Inversion, Eduardo C. Balreira
Incompressibility And Global Inversion, Eduardo C. Balreira
Eduardo Cabral Balreira
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.