4 problems

Let $(M,g)$ be a smooth Riemannian manifold of Anosov type. For symmetric $m$-tensors, let $I_m^g$ be the X-ray transform, and call it solenoidal injective when … Here $D_g$ is the…

Let $(M_1,g_1)$ and $(M_2,g_2)$ be smooth Riemannian manifolds of Anosov type whose boundary metrics agree: … Let $(\ell_g,S_g)$ denote the lens data. Lens rigidity conjecture. If…

Let $M$ be a smooth manifold with boundary, and let $g_1$ and $g_2$ be smooth metrics of Anosov type on $M$ such that … Assume that $g_1$ and $g_2$ have the same marked lens data,…

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