Related papers: Higher-Rank Radon Transforms on Constant Curvature…

There is a hierarchy of commuting soliton equations associated to each symmetric space U/K. When U/K has rank n, the first n flows in the hierarchy give rise to a natural first order non-linear system of partial diffferential equations in n…

We use 5-brane webs to study the two-dimensional space of supersymmetric mass deformations of higher rank generalizations of the 5d $E_1$ and $\tilde{E}_1$ theories. Some of the resulting IR phases are described by IR free supersymmetric…

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The…

We consider the X-ray transform in a projective space over a finite field. It is well known (after E. Bolker) that this transform is injective. We formulate an analog of I.M. Gelfand's admissibility problem for the Radon transform, which…

We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces $G/H$, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an…

We introduce a curvature-dimension condition for autonomous Lagrangians on weighted manifolds, which depends on the Euler-Lagrange dynamics on a single energy level. By generalizing Klartag's needle decomposition technique to the Lagrangian…

We derive an explicit inversion algorithm for the spherical Radon transform in odd dimensions with partial radial data. We prove that the reconstruction of the unknown function can be reduced to solving ordinary differential equations,…

We show well-posedness for the parabolic Anderson model on $2$-dimensional closed Riemannian manifolds. To this end we extend the notion of regularity structures to curved space, and explicitly construct the minimal structure required for…

Meridian surfaces in the Euclidean 4-space are two-dimensional surfaces which are one-parameter systems of meridians of a standard rotational hypersurface. On the base of our invariant theory of surfaces we study meridian surfaces with…

Recovering a function from its spherical Radon transform with centers of spheres of integration restricted to a hypersurface is at the heart of several modern imaging technologies, including SAR, ultrasound imaging, and photo- and…

If $G$ is a finite group, is a function $f:G\to\mathbb C$ determined by its sums over all cosets of cyclic subgroups of $G$? In other words, is the Radon transform on $G$ injective? This inverse problem is a discrete analogue of asking…

We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three…

In this note, we study the resonance variety of rank-two vector bundles over an elliptic curve. Our approach is based on analyzing the flattening stratification of the resonance. We also investigate the linear section of the Grassmann…

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work…

Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…

In this paper we introduce and study a new class of varifolds in $\mathbf{R}^{n+1}$ of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon…

Concerning the problem of classifying complete submanifolds of Euclidean space with codimension two admitting genuine isometric deformations, until now the only known examples with the maximal possible rank four are the real Kaehler minimal…

We address the problem of determining the hypersurfaces $f\colon M^{n} \to \mathbb{Q}_s^{n+1}(c)$ with dimension $n\geq 3$ of a pseudo-Riemannian space form of dimension $n+1$, constant curvature $c$ and index $s\in \{0, 1\}$ for which…

Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…

The main focus of the paper is the investigation of moduli space of left invariant pseudoRiemannian metrics on the cotangent bundle of Heisenberg group. Consideration of orbits of the automorphism group naturally acting on the space of the…