Injectivity of non-singular planar maps with one convex component

TL;DR

This paper proves that any non-singular planar map with at least one convex component is injective, without requiring strict convexity, advancing understanding of planar map properties.

Contribution

It establishes injectivity of non-singular planar maps with convex components without assuming strict convexity, a novel generalization.

Findings

Non-singular planar maps with convex components are injective

Injectivity holds without strict convexity assumption

Advances understanding of planar map properties

Abstract

We prove that if a non-singular planar map $\Lambda \in C^2(R^2,R^2)$ has a convex component, then $\Lambda$ is injective. We do not assume strict convexity.