4 problems

Quantitative maximal local rewinding volume rigidity conjecture. There exists $\epsilon(n,\rho)>0$ such that, for every $0<\epsilon<\epsilon(n,\rho)$, these assumptions imply that…

Let $M$ be an orientable cusped hyperbolic $3$-manifold. Let $X_n$ be the geometric component of the character variety with target group $\mathrm{PGL}(n,\mathbf C)$, and let…

Let $n=2k+1>4$ be odd, and let $\Gamma$ be a discrete subgroup of $\operatorname{SO}_0(n-1,2)$ acting freely, properly discontinuously and cocompactly on anti-de Sitter space…

Let $Z$ be a compact metric space of Hausdorff dimension $n$, let $X$ be a metric space, and let $f:Z\to X$ be a distance non-increasing onto map. Assume that $X$ and $Z$ are Alexa…