5 problems

Benedetti–Guadagnini conjecture. For every $\gamma\in\pi_1(M)$,

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

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 $(X_1,d_1)$ 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…

Burns–Katok conjecture. The marked length spectrum map $L$ is injective.