On local diffeomorphisms ofR n that are injective

Abstract

There are obtained conditions under which maps fromR n to itself are globally injective. In particular there are proved some partial results related to the Weak Markus-Yamabe Conjecture which states that if a vector field X:R n →R n has the property that, for allp ∈R n , all the eigenvalues ofD X (p) have negative real part, thenX has at most one singularity.