相关论文: Radon transform and curvature
We define Radon transform and its inverse on the two-dimensional anti-de Sitter space over local fields using a novel construction through a quadratic equation over the local field. We show that the holographic bulk reconstruction of…
We consider the Radon transform associated to dual pairs $(X,\Xi)$ in the sense of Helgason, with $X=G/K$ and $\Xi=G/H$, where $G=\mathbb{R}^d\rtimes K$, $K$ is a closed subgroup of ${\rm GL}(d,\mathbb{R})$ and $H$ is a closed subgroup of…
In this article we study the spherical mean Radon transform in $\mathbf R^3$ with detectors centered on a plane. We use the consistency method suggested by the author of this article for the inversion of the transform in 3D. A new iterative…
In 1927 Philomena Mader derived elegant inversion formulas for the hyperplane Radon transform on $\bbr^n$. These formulas differ from the original ones by Radon and seem to be forgotten. We generalize Mader's formulas to totally geodesic…
In this article, we give a unified proof of the end-point estimates of the totally-geodesic $k$-plane transform of radial functions on spaces of constant curvature. The problem of getting end-point estimates is not new and some results are…
We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions…
The Radon transform is a bounded operator from L^p of Euclidean space R^d to L^q of the Grassmann manifold of all affine hyperplanes in R^d, for certain exponents. We identify all extremizers of the associated inequality for the endpoint…
We obtain explicit inversion formulas for the Radon-like transform that assigns to a function on the unit sphere the integrals of that function over hemispheres lying in lower dimensional central cross-sections. The results are applied to…
In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…
The well known formulas express the curvature and the torsion of a curve in $R^3$ in terms of euclidean invariants of its derivatives. We obtain expressions of this kind for all curvatures of curves in $R^n$. It follows that a curve in…
We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.
In this article, using the generalized Newton transformation, we define higher order mean curvatures of distributions of arbitrary codimension and we show that they agree with the ones from Brito and Naveira (Ann. Global Anal. Geom. 18,…
Let $G_{n,r}(\bbK)$ be the Grassmannian manifold of $k$-dimensional $\bbK$-subspaces in $\bbK^n$ where $\bbK=\mathbb R, \mathbb C, \mathbb H$ is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine…
The transform considered in the paper averages a function supported in a ball in $\RR^n$ over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic…
We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a…
We study integral transforms mapping a function on the Euclidean plane to the family of its integration on plane curves, that is, a function of plane curves. The plane curves we consider in the present paper are given by the graphs of…
The main result of this paper is a convexity estimate for translating solitons of extrinsic geometric flows which evolve under a $1$-homogeneous concave function in the principal curvatures. In addition, we show examples of these…
Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of…
We suggest new modifications of Helgason's support theorems and descriptions of the kernels for several projectively equivalent transforms of integral geometry. The paper deals with the hyperplane Radon transform and its dual, the totally…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…