Behavior on level sets and global inversion

Abstract

In this paper, we give a necessary and sufficient condition for diffeomorphism of onto itself (Theorem 7), under the assumption that it is already a local diffeomorphism . This is a generalization of a result of Sabatini to all dimensions. We also obtain two results of Balreira from our main results.

Keywords:

• diffeomorphism
• global inversion
• global injectivity

AMS Subject Classifications:

• 57R50
• 58C25

Acknowledgements