3 problems

Finite-volume most-symmetry conjecture. Proposition 1 remains true when $M$ has finite volume and $h$ is any finite-volume Riemannian metric; that is, $\operatorname{Isom}(M,h)$ sh…

Peripheral topology conjecture. $M$ cannot be homotoped to be contained in a collar neighborhood of $\partial\overline{M}$.

Let $M$ be a noncompact, complete, finite volume manifold with sectional curvature $K(M)<0$, and let $\widetilde{M}$ be its universal cover. An embedded half flat is an embedded co…