7 problems

Let $cmathcal{M}$ be a compact hyperbolic manifold of dimension $n eq 3$. Belolipetsky–Emery conjecture. There exists a noncompact hyperbolic $n$-manifold $cmathcal{M}1$ whose…

Let $M^n$ be a manifold, and let $\text{MinVol}(M)$ denote the infimum of the volumes of complete metrics on $M$ with $|\text{sec}_M|\le 1$. Gromov's gap conjecture. There exists a…

Let $M$ be a compact complex surface of general type, and let $\operatorname{Vol}_{K}(M)$ and $\operatorname{Vol}_{s}(M)$ denote its minimal volume defined using sectional curvatur…

Let $M$ be a manifold admitting a finite-volume hyperbolic metric, and let ${\rm MinVol}(M)$ denote the infimum of ${\rm Vol}(M,g)$ over complete Riemannian metrics $g$ on $M$ whos…

Let $(M^n,g_0)$ be a complete hyperbolic manifold with finite volume, where $g_0$ is a hyperbolic metric on $M^n$. The minimal volume of $M$ is denoted by … Gromov's conjecture. Fo…

The section concerns finite-volume hyperbolic $n$-orbifolds, including compact and noncompact arithmetic orbifolds and their minimal volumes, as well as the related Euler-character…

Let $M^n$ be a closed smooth $n$-manifold. Write $\operatorname{MinVol}(M)$ for the infimum of $\operatorname{vol}_g(M)$ over all smooth complete Riemannian metrics $g$ on $M$ whos…