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.
Plane Delaunay triangulations are rigid under Luo's discrete conformal change.
This paper completes the classification of discrete conformal structures on surfaces.
We study surfaces with decorations and prove uniformization in non-Euclidean geometries.
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…
The paper proves convergence of discrete maps to Riemann mappings for polyhedral surfaces.
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…
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…
Paper proves rigidity of discrete conformal structures on polyhedral surfaces.
Plane triangulations remain rigid under discrete conformal changes.
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…
New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.
This paper classifies discrete conformal structures on surfaces with boundary.
Discrete conformal maps on surfaces with vertex decorations are studied.
The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.
Discrete Laplacians defined for spherical and hyperbolic surfaces.
Fractional combinatorial flow improves surface conformal structures.
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…
New boundary and point constraints for controlling conformal surfaces.
Conformal qc geometry of spherical qc manifolds are investigated. We construct the qc Yamabe operators on qc manifolds, which are covariant under the conformal qc transformations. A qc manifold is scalar positive, negative or vanishing if and only if its qc Yamabe invariant is positive, negative or zero, respectively. …
This paper is the the third part of a series of paper whose aim is to use of the framework of \emph{twisted spectral triples} to study conformal geometry from a noncommutive geometric viewpoint. In this paper we reformulate the inequality of Vafa-Witten \cite{VW:CMP84} in the setting of twisted spectral triples. This i…
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is disc…
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk patterns by optimizing an objective function, which turns out to be intimately …
New geometric interpretation of discrete Willmore energy using rolling spheres connection.
Paper improves estimates for discrete Laplace in hyperbolic geometry.
We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,Γ) where K is a Kaehler manifold and Γa discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invari…
We consider the interpretation in classical geometry of conformal field theories constructed from orbifolds with discrete torsion. In examples we can analyze, these spacetimes contain ``stringy regions'' that from a classical point of view are singularities that are to be neither resolved nor blown up. Some of these mo…
New theorem proves convergence of various discrete conformal structures to conformal maps.
Generalized meshes for non-regular geometries, including fractures.
Extends rigidity and existence results for discrete conformal structures on surfaces with boundary.
The paper proves rigidity and ergodicity of horospherical foliations.
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.
This is a second paper in a series devoted to the minimal unitary representation of O(p,q). By explicit methods from conformal geometry of pseudo-Riemannian manifolds, we find the branching law corresponding to restricting the minimal unitary representation to natural symmetric subgroups. In the case of purely discrete…
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.
Discrete maximal surfaces identified from s-embeddings.
New method approximates Gaussian curvature on discrete surfaces.
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isoth…
Survey on discrete minimal surfaces and their properties.
In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (that comes with spin transformations to comformally transfrom immersions) and the two are naturally related. In this paper we consider a corresponding pair of disc…
The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.
Unique metric found for discrete curvature on spherical cone-metrics.
Random Gaussian fields on 4D Riemannian manifolds with conformal invariance.
CP uses geometric information to improve conformal prediction robustness.
In this article and in its sequel we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamics on certain infinite-dimensional …
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as the geometry varies in a particular way, which we call a conformal variation. This…
Let X be a Hadamard manifold and a discrete group of isometries of X which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the geometric limit set of in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessar…
Study BGG operators on homogeneous conformal geometries.