2 problems

Let $F:\mathbb{R}^n\to\mathbb{R}^n$ be a $C^1$ map. Chamberland–Meisters' injectivity conjecture. Suppose there exists an $\varepsilon>0$ such that … for every eigenvalue $\lambda$…

Nollet–Xavier conjecture. If the pre-image $f^{-1}(H)$ of every affine hyperplane $H\subseteq\mathbb{R}^n$ is connected, possibly empty, then $f$ is injective.