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.
New theorem proves convergence of various discrete conformal structures to conformal maps.
Plane triangulations remain rigid under discrete conformal changes.
Plane Delaunay triangulations are rigid under Luo's discrete conformal change.
Extends rigidity and existence results for discrete conformal structures on surfaces with boundary.
This paper completes the classification of discrete conformal structures on surfaces.
We establish a connection between two previously unrelated topics: a particular discrete version of conformal geometry for triangulated surfaces, and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated surfaces are considered discretely conformally equivalent if the edge lengths are related by s…
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying …
Study on deforming discrete conformal structures on surfaces with boundaries.
The paper proves convergence of discrete maps to Riemann mappings for polyhedral surfaces.
Discrete conformal maps on surfaces with vertex decorations are studied.
We establish a connection between recent developments in the study of vortices in the abelian Higgs models, and in the theory of structure-preserving discrete conformal maps. We explain how both are related via conformal mapping problems involving prescribed linear combinations of the curvature and volume form, and sho…
Study on discrete Gaussian curvature for polyhedral surfaces.
New method approximates Gaussian curvature on discrete surfaces.
This paper classifies discrete conformal structures on surfaces with boundary.
New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.
The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.
The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.
We study surfaces with decorations and prove uniformization in non-Euclidean geometries.
Finding appropriate notions of discrete holomorphic maps and, more generally, conformal immersions of discrete Riemann surfaces into 3-space is an important problem of discrete differential geometry and computer visualization. We propose an approach to discrete conformality that is based on the concept of holomorphic l…
Paper proves rigidity of discrete conformal structures on polyhedral surfaces.
The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of…
Unique metric found for discrete curvature on spherical cone-metrics.
Fractional combinatorial flow improves surface conformal structures.
A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an isometric embedding into the background geometry with the chosen edge lengths. Ad…
The paper proves a theorem for discretizing Gaussian curvature on surfaces.
New boundary and point constraints for controlling conformal surfaces.
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature polyhedral metric which is unique up to scaling. Furthermore, the constant curvature me…
New interpretation of discrete conformality using polyhedral convex hulls.
Extremal length is a conformal invariant that transfers naturally to the discrete setting, giving square tilings as a natural combinatorial analog of conformal mappings. Recent work by S. Hersonsky has explored generalizing these ideas to three-dimensional cube tilings. The connections between discrete extremal length …
Liouville's theorem says that in dimension greater than two, all conformal maps are Möbius transformations. We prove an analogous statement about simplicial complexes, where two simplicial complexes are considered discretely conformally equivalent if they are combinatorially equivalent and the lengths of corresponding …
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is propo…
The paper introduces a new discretization of Gaussian curvature on surfaces.
Discrete approximation solves Björling's minimal surface problem.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
The elastic flow, which is the -gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples in…
Discrete Laplacians defined for spherical and hyperbolic surfaces.
The paper develops methods to estimate frequencies in large discrete data sets with improved coverage and robustness.
Proves existence of unique circle packings on polyhedral surfaces.
Polyconvex energies with conformal invariance have smooth stationary points outside a discrete set.
Improved rigidity of Delaunay triangulated plane.
The paper tackles prescribing discrete Gaussian curvature on polyhedral surfaces.
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the m…
Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the …
The paper proves rigidity and ergodicity of horospherical foliations.
A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of Darboux transforms of polarized curves in the conformal n-sphere and their transformation theory is studied. Semi-discre…
A discrete conformal map (DCM) maps the square lattice to the Riemann sphere such that the image of every irreducible square has the same cross-ratio. This paper shows that every periodic DCM can be determined from spectral data (a hyperelliptic compact Riemann surface, called the spectral curve, equipped with some mar…
A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending energy for discrete thin-shells is derived.