4 problems

Let $\mathbb{F}$ be a field, let $G$ be a loopless graph with orientation $D$, and let $\psi$ and $\psi'$ be $(\mathbb{F}^+\rtimes \mathbb{F}^{\times})$-gain functions for $G$. Sup…

Let $g_1$ and $g_2$ be conformal sub-Riemannian metrics on $(M,D)$, so that … for a nonvanishing smooth function $\alpha:M\to\mathbb{R}$. They are constantly proportional if…

Let $U\in\mathcal{G}_k\mathcal{P}_n$ admit a basis of top powers, and let $W(U)$ denote its Wronskian covariant. The notation $U^{(\ell-1)}$ denotes the associated derived subspace…

Let $M^n$ be a closed connected manifold, and let $g$ and $\bar g$ be Riemannian metrics on $M^n$ that are projectively equivalent and nonproportional. Geodesic rigidity conjecture…