3 problems

Let $\mathbb{B}^n$ be the unit ball, let $\overline{\mathbb{R}}^n$ be the one-point compactification of $\mathbb{R}^n$, and let $q$ denote the chordal metric. For…

Let $f=(f_1,\ldots,f_m):\mathbb{Z}_k^n\to\mathbb{Z}_l^m$ be $\alpha$-Lipschitz with respect to the $L^1$ norm. Coordinatewise junta conjecture. For every $\delta,\epsilon>0$, at le…

Let $G=\mathrm{PO}(n,1)$, let $\Gamma_0$ be the group in the representation space under consideration, and let $(j,\rho)\in\operatorname{Hom}(\Gamma_0,G)^2$. For $n=2$, assume that…