5 problems

Let $(M,g)$ be a closed Riemannian manifold with negative sectional curvature, of dimension $n\geq 3$. An immersed totally geodesic submanifold $N$ in $M$ is maximal if it is not c…

Let $(M,g)$ be a closed Riemannian manifold with negative sectional curvature, of dimension $n\geq 3$. An immersed totally geodesic submanifold $N$ in $M$ is maximal if it is not c…

Large totally geodesic hypersurface rigidity conjecture. For every $D>0$ and $k\in\mathbb{N}$, there exists $A=A(D,k)$ such that if $N$ contains a totally geodesic hyperbolic hyper…

Type-IV total geodesy conjecture. Then

Rank-2 type-I total geodesy conjecture. If