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.
Study reconstructs Riemannian metric from Cherenkov radiation in complex media.
The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. The…
We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, i…
Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct time…
Generalizes Fermat's principle for wave propagation in cone structures.
Study on droplet flow on uneven surfaces, proving existence and properties.
A new model uses Lorentz-Finsler geometry to predict wave propagation.
We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordina…
GPR enhances materials discovery by automating parameter space exploration.
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
Deep learning has exhibited superior performance for various tasks, especially for high-dimensional datasets, such as images. To understand this property, we investigate the approximation and estimation ability of deep learning on anisotropic Besov spaces. The anisotropic Besov space is characterized by direction-depen…
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theo…
Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.
We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. By means of the limiting absorption principle, a Fredholm alterna…
We survey some results on travel time tomography. The question is whether we can determine the anisotropic index of refraction of a medium by measuring the travel times of waves going through the medium. This can be recast as geometry problems, the boundary rigidity problem and the lens rigidity problem. The boundary r…
Wave propagation framework using cone structures and observers' vector fields.
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand side data from some polynomially weighted Sobolev spaces and obtain solutions whi…
Study spherical doubly warped spacetimes for stellar collapse and cosmology.
In this paper, we investigate a holonomy invariant elliptic anisotropic surface energy for hypersurfaces in a complete Riemannian manifold, where "holonomy invariant" means that the elliptic parametric Lagrangian (i.e., a Finsler metric) of the Riemannian manifold used to define the anisotropic surface energy is consta…
Paper proves anisotropic Minkowski inequality and related inequalities.
New Kelvin transform for anisotropic elliptic problems.
Paper solves anisotropic capillary Minkowski problem for p ≥ 1.
Paper proves rigidity results for anisotropic capillary hypersurfaces.
Paper solves Minkowski problem for anisotropic p-torsional rigidity.
Study magnetic field evolution in inhomogeneous axion stars.
Anisotropic min-max theory constructs stable minimal surfaces in 3-manifolds.
Unique ancient solutions found for anisotropic curve shortening flow.
Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
Researchers describe a specific type of submanifolds in Euclidean space.
Formula proves monotonicity for anisotropic minimal hypersurfaces.
In this paper, we study the anisotropic Minkowski problem. It is a problem of prescribing the anisotropic Gauss-Kronecker curvature for a closed strongly convex hypersurface in Euclidean space as a function on its anisotropic normals in relative or Minkowski geometry. We first formulate such problem to a Monge-Ampére t…
We introduce a new parameter to measure the inhomogeneity of training datasets.
We introduce the anisotropic tensor calculus, which is a way of handling with tensors that depend on the direction remaining always in the same class. This means that the derivative of an anisotropic tensor is a tensor of the same type. As an application, we show how to define derivations using anisotropic linear conne…
Sharp threshold found for Frechet mean of inhomogeneous graphs.
A general approach to formulation of supergravity in higher order anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) is given. We analyze three models of locally anisotropic supergravity.
Develops a PDE approach to constructing nontrivial anisotropic surfaces.
Paper studies stability of curved surfaces in a half-space.
Characterizes paths minimizing anisotropic lengths in Euclidean space.
Anisotropic minimal graphs over half-spaces are flat.
Study anisotropic flow for capillary hypersurfaces, proving new inequalities.
In this note, we give a classification of complete anisotropic isoparametric hypersurfaces, i.e., hypersurfaces with constant anisotropic principal curvatures, in Euclidean spaces, which is in analogue with the classical case for isoparametric hypersurfaces in Euclidean spaces. On the other hand, by an example of local…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
Graphs with bounded anisotropic mean curvature are regular almost everywhere.
We study surfaces with constant anisotropic mean curvature which are invariant under a helicoidal motion. For functionals with axially symmetric Wulff shapes, we generalize the recently developed twizzler representation of Perdomo to the anisotropic case and show how all helicoidal constant anisotropic mean curvature s…
Study anisotropic capillary surfaces in a wedge using generalized Minkowski norms.
The study finds anisotropic minimal surfaces in 3-manifolds with smooth boundaries.
Study on Gauss map of anisotropic minimal surfaces with Morse index estimates.