3 problems

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 $(M^n,g_0)$ 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…

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…