We consider Calderón's inverse problem with partial data in dimensions n≥ 3. If the
inaccessible part of the boundary satisfies a (conformal) flatness condition in one direction …

We prove a uniqueness result for the broken ray transform acting on the sums of functions
and 1-forms on surfaces in the presence of an external force and a reflecting obstacle. We …

Given, a compact connected Riemannian manifold of dimension, with boundary, we study
the inverse boundary value problem of determining a time-dependent potential, appearing …

We study ray transforms on spherically symmetric manifolds with a piecewise $ C^{1, 1} $
metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $ L …

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle,
following earlier work of Mukhometov. If the surface has nonpositive curvature and the …

We show injectivity of the X-ray transform and the d d-plane Radon transform for
distributions on the n n-torus, lowering the regularity assumption in the recent work by …

arxiv:2410.04908v1 [math.DG] 7 Oct 2024 Page 1 arxiv:2410.04908v1 [math.DG] 7 Oct 2024
SURVEY ON BROKEN RAY TRANSFORMS SHUBHAM R. JATHAR AND JESSE RAILO …

We reduce boundary determination of an unknown function and its normal derivatives from
the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic …

We study the broken ray transform on $ n $-dimensional Euclidean domains where the
reflecting parts of the boundary are flat and establish injectivity and stability under certain …

We study the integral transform over a general family of broken rays in $\mathbb {R}^ 2$. It is
natural for broken rays to have conjugate points, for example, when they are reflected from a …