Related papers: Support theorem for the transverse ray transform o…

Let $(M,g)$ be a simple Riemannian manifold with boundary and consider the geodesic ray transform of symmetric 2-tensor fields. Let the integral of $f$ along maximal geodesics vanish on an appropriate open subset of the space of geodesics…

Let $(M,g)$ be a simple Riemannian manifold. Under the assumption that the metric $g$ is real-analytic, it is shown that if the geodesic ray transform of a function $f\in L^{2}(M)$ vanishes on an appropriate open set of geodesics, then…

In this paper we study the local magnetic ray transform of symmetric tensor fields up to rank two on a Riemannian manifold of dimension $\geq 3$ with boundary. In particular, we consider the magnetic ray transform of the combinations of…

Consider a Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem…

Consider a compact Riemannian manifold in dimension $n$ with strictly convex boundary. We show the local invertibility near a boundary point of the transverse ray transform of $2$ tensors for $n\geq 3$ and the mixed ray transform of $2+2$…

Consider a compact Riemannian manifold in dimension $n\geq 3$ with strictly convex boundary. We show that the transverse ray transform of $1$ tensors and the mixed ray transform of $1+1$ tensors are invertible, up to natural obstructions,…

We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a symmetry condition at the reflecting part of the boundary and…

In this article, we study the microlocal properties of the geodesic ray transform of symmetric $m$-tensor fields on 2-dimensional Riemannian manifolds with boundary allowing the possibility of conjugate points. As is known from an earlier…

We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n>=3. We also present…

We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean 3-space, using data from rotation about three orthogonal axes. We show…

This article is concerned with support theorems of the X-ray transform on non-compact manifolds with conjugate points. In particular, we prove that all simply connected 2-step nilpotent Lie groups have a support theorem. Important…

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic 1-form…

We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.

We prove injectivity and a support theorem for the X-ray transform on $2$-step nilpotent Lie groups with many totally geodesic $2$-dimensional flats. The result follows from a general reduction principle for manifolds with uniformly…

We consider convolution equations of the type f * T = g where f, g are in L^p(R^n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T we show that f is compactly supported,…

Dedicated to Professor Gromoll: The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle…

We study light ray transform of symmetric 2-tensor fields defined on a bounded time-space domain in $\mathbb{R}^{1+n}$ for $n\geq 3$. We prove a uniqueness result for such light ray transforms. More precisely, we characterize the kernel of…

We prove a support theorem for the radiation fields on asymptotically Euclidean manifolds with metrics which are warped products near infinity. It generalizes to this setting the well known support theorem for the Radon transform on…

Recently we generalized Toponogov's comparison theorem to a complete Riemannian manifold with smooth convex boundary, where a geodesic triangle was replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a…

We define and characterise small support for complexes over non-Noetherian rings and in this context prove a vanishing theorem for modules. Our definition of support makes sense for any rigidly compactly generated tensor triangulated…