Incompressibility and global inversion

Eduardo Cabral Balreira

Abstract


Given a local diffeomorphism $f\colon \mathbb{R}^n\to \mathbb{R}^n$, we consider
certain incompressibility conditions on the parallelepiped
$Df(x)([0,1]^n)$ 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.

Keywords


Global injectivity; global invertibility; Hadamard's theorem

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