A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper calculates transformation operators and proves a theorem on 4D manifolds.
Unified proof of smooth fibration theorems for collapsed manifolds.
The paper proves a transformation theorem under a monotone property of almost Euclidean factors of geodesic balls.
In this paper we prove a new inversion theorem and a refinement of an old support theorem for two Radon transforms on a symmetric space. Included are some new identities for the Abel transform and some results about the Fourier transform from a joint work with Rawat, Sengupta and Sitaram.
Theorems adapted for prequantum systems, showing symplectomorphism and gauge transformation.
A theorem transforms Lorentzian to signature-changing metrics.
New integral theorems improve density function estimations.
Geometric transformations on null curves in AdS induce KdV solutions.
X-ray transform on H-type groups solved, revealing function injectivity.
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.
Transformed geometry into algebra to prove Pick's theorem efficiently.
The study establishes uncertainty principles on harmonic manifolds of rank one.
Researchers find explicit Bäcklund transforms for specific quadrics.
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 ingredients of the proof are the concept of plane covers and a support theorem for simple…
Develops support theorem for analytic transforms in tomography.
We discuss the Ribaucour transformation of Legendre maps in Lie sphere geometry. In this context, we give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer--Tojeiro. We go on to formulate and prove a higher dimensional version of the Permutability Theorem. It is sho…
Study X-ray transform on manifolds, desingularize, and improve mapping properties.
Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed, we obtain the following complex generalisation of Wigner's theorem: a holomorph…
We prove two injectivity theorems for the geodesic ray transform on two-dimensional, complete, simply connected Riemannian manifolds with non-positive Gaussian curvature, also known as Cartan-Hadamard manifolds. The first theorem is concerned with bounded non-positive curvature and the second with decaying non-positive…
Paper solves injectivity of X-ray transform on surfaces.
We complete the microlocal study of the geodesic X-ray transform on Riemannian manifolds with Anosov geodesic flow initiated by Guillarmou and pursued by Guillarmou and the second author. We prove new stability estimates and clarify some properties of the operator , the generalized X-ray transform. These estimates…
The Hopf-Rinow theorem is extended to sub-Finslerian geometry.
We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutabili…
In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of Bäcklund transformations. We then showed how this construction can be applied to construct Bäcklund transformation between equations which are Darboux integrable. Here we give a number of detailed examples and new …
The conformal geometry of spacelike surfaces in 4-dimensional Lorentzian space forms has been studied by the authors in a previous paper, where the so-called polar transform was introduced. Here it is shown that this transform preserves spacelike conformal isothermic surfaces. We relate this new transform with the know…
Injective X-ray transform on Heisenberg group for regular functions.
We classify the simplest rational elements in a twisted loop group, and prove that dressing actions of them on proper indefinite affine spheres give the classical Tzitzéica transformation and its dual. We also give the group point of view of the Permutability Theorem, construct complex Tzitzéica transformations, and di…
We prove that the Fourier--Laplace--Nahm transform for connections on the projective line is a hyper-Kähler isometry.
In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of Möbius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.
We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong additivity properties. In the case of cobordisms between manifolds with boundary, we pr…
NAST generalizes scattering transform for non-stationary time series analysis.
Embeds Riemannian manifolds with Anosov flows, linking classical and new theorems.
Study spherical Fourier transform on hypergeometric type harmonic manifolds.
We obtain a reduction of the vectorial Ribaucour transformation that preserves the class of submanifolds of constant sectional curvature of space forms, which we call the -transformation. It allows to construct a family of such submanifolds starting with a given one and a vector-valued solution of a system of linear…
New proof of Lie-Tresse theorem with computational advantages.
Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse …
Transformers model contextual relations using probabilistic measures, revealing their expressive power.
We investigate geometric aspects of the the Bäcklund transform of principal contact element nets. A Bäcklund transform exists if and only if it the principal contact element net is of constant negative Gaussian curvature (a pseudosphere). We describe an elementary construction of the Bäcklund transform and prove its co…
New form of -singularities for fronts in 3D space.
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the …
The version of Marsden-Ratiu reduction theorem for Nambu-Poisson manifolds by a regular distribution has been studied by Ibez et al. In this paper we show that the reduction is always ensured unless the distribution is zero. Next we extend the more general Falceto-Zambon Poisson reduct…
The study bounds quantum eigenfunctions on complex manifolds.
Unified theorem for deep and shallow joint-equivariant machines.
We derive a permutability theorem for the Christoffel, Goursat and Darboux transformations of isothermic surfaces. As a consequence we obtain a simple proof of a relation between Darboux pairs of minimal surfaces in Euclidean space, curved flats in the 2-sphere and flat fronts in hyperbolic space.
In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jaco…
We prove an analog of Cartan's theorem, saying that the chain-preserving transformations of the boundary of the quaternionic hyperbolic spaces are projective transformations. We give a counting and equidistribution result for the orbits of arithmetic chains in the quaternionic Heisenberg group.
Transformers are explained as infinite-dimensional kernel machines.
The classical Liouville Theorem on conformal transformations determines local conformal transformations on the Euclidean space of dimension . Its natural adaptation to the general framework of Riemannian structures is the 2-rigidity of conformal transformations, that is such a transformation is fully determined…