8 problems

Let $M$ be a smooth closed manifold, and let $g$ and $g_0$ be negatively curved metrics, or more generally metrics whose geodesic flows are Anosov. Let $\mathcal L_g$ denote the ma…

Let $X$ be a closed manifold, and let $h_1$ and $h_2$ be Riemannian metrics on $X$ with negative sectional curvature. For each such metric, let $\mathrm{MLS}_h$ assign to every con…

Let $(M,g)$ be a closed Riemannian manifold with all sectional curvatures negative, let $\Gamma=\pi_1(M)$, and let $C_\Gamma$ be the set of conjugacy classes of non-trivial element…

Croke–Dairbekov–Sharafutdinov marked-length-spectrum volume conjecture. The inequality

Let $(X_1,d_1)$ and $(X_2,d_2)$ be negatively curved Hadamard manifolds, and let $\Gamma$ be a torsion-free group acting properly discontinuously and co-compactly on $X_1$ and…

Let $M$ be a closed, connected manifold, and let $g$ and $g'$ be negatively curved Riemannian metrics on $M$. For each free homotopy class $d70e$, let $\operatorname{MLS}_g(d70e)$…

Approximate marked length spectrum rigidity conjecture. The result proved in the paper should hold for all hyperbolic groups and pairs of finite generating sets $S,S_\ast$ if the e…

Marked length spectrum conjecture. If $M_0$ and $M_1$ have the same marked length spectrum, then they are isometric, and the isomorphism of fundamental groups is induced by an isom…