4 problems

Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be a $C^1$ map, and let $J(f)$ denote its Jacobian matrix. The $C^1$ stability conjecture. If the eigenvalues of $J(f)$ have strictly negative r…

Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be a $C^1$ map, and let $J(f)$ denote its Jacobian matrix. A matrix is unipotent when all its eigenvalues are $1$. The $C^1$ unipotent Jacobian…

Neural Jacobian Conjecture. For every $F\in\mathcal N_{n,N}^+$, the map $F$ is globally injective.

Surjectivity conjecture. If $J(F)$ is nowhere vanishing and $\operatorname{codim} S_F\geq2$, then