5 problems

Let $(M,g)$) be a simple Riemannian manifold and let $f$ be a symmetric $m$-tensor field, written in local coordinates as … Define its geodesic ray transform by … where…

Let $(M,g)$ be a simple Riemannian manifold and let $f$ be a symmetric $2$-tensor field. Its geodesic ray transform is … where $\gamma:[0,l(\gamma)]\to M$ is a geodesic connecting…

Let $(M,g_0)$ be a smooth closed Riemannian manifold with Anosov geodesic flow, and let $I^{g_0}_2$ be the X-ray transform on symmetric two-tensors, defined by … Here $D^*$ is the…

Let $(M,g)$ be a compact nontrapping surface with strictly convex boundary. For a smooth symmetric $m$-tensor field $f$ on $M$, let $I_m f$ denote its ray transform. A tensor field…

S-injectivity conjecture. The geodesic ray transform $I$ is s-injective on every simple Riemannian manifold.