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.
Properness proven for circle packings and Delaunay patterns on complex projective structures.
Plane Delaunay triangulations are rigid under Luo's discrete conformal change.
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 …
In this thesis a connection between the worlds of discrete and continuous conformal geometry is explored. Specifically, a disk pattern production theroem is proved using an energy which measures how ``uniform'' the angle data of a triangulation is, see also math.DG/0002150. Then this energy is averaged over all the Del…
We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal circle patterns are associated to hyperideal hyperbolic polyhedra. We describe the…
Study circle patterns and polyhedral surfaces in hyperbolic ends, proving manifold properties.
A Delaunay cell decomposition of a surface with constant curvature gives rise to a circle pattern, consisting of the circles which are circumscribed to the facets. We treat the problem whether there exists a Delaunay cell decomposition for a given (topological) cell decomposition and given intersection angles of the ci…
The study connects triangulated surfaces to complex projective structures and circle patterns.
Convex iso-Delaunay regions found in flat surface strata.
New types of Delaunay hypersurfaces found in spheres.
Delaunay has shown that the Delaunay complex of a finite set of points of Euclidean space triangulates the convex hull of , provided that satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be defined for arbitrary Riemannian manifolds. However, Delaunay's generic…
Stable 2-lobed Delaunay tori found in 3-sphere.
DTL uses Delaunay triangulation for nonparametric function approximation.
Given a lattice L of R^n, a polytope D is called a Delaunay polytope in L if the set of its vertices is S\cap L where S is a sphere having no lattice points in its interior. D is called perfect if the only ellipsoid in R^n that contains S\cap L is exactly S. For a vector v of the Leech lattice Λ_{24} we define Λ_{24}(v…
We consider constant mean curvature 1 surfaces in arising via the DPW method from a holomorphic perturbation of the standard Delaunay potential on the punctured disk. Kilian, Rossman and Schmitt have proven that such a surface is asymptotic to a Delaunay surface. We consider families of such potentials p…
Improved rigidity of Delaunay triangulated plane.
The study identifies unique Delaunay surfaces with constant mean curvature.
The article discusses how to create a special type of triangle mesh for surfaces in 3D space.
The generalized Weierstrass representation is used to analyze the asymptotic behavior of a constant mean curvature surface that arises locally from an ordinary differential equation with a regular singularity. We prove that a holomorphic perturbation of an ODE that represents a Delaunay surface generates a constant mea…
Classical Delaunay surfaces are highly symmetric constant mean curvature (CMC) submanifolds of space forms. We prove the existence of Delaunay-type hypersurfaces in a large class of compact manifolds, using the geometry of cohomogeneity one group actions and variational bifurcation techniques. Our construction speciali…
Given a finite set of points in and a radius parameter, we study the Čech, Delaunay-Čech, Delaunay (or Alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four…
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with …
Hexagonal triangulation remains rigid under certain conditions.
Minimal Delaunay triangulations on hyperbolic surfaces have linear number of vertices.
The paper constructs solutions to a critical Dirac equation on spheres.
A finite subset S of a closed hyperbolic surface F canonically determines a "centered dual decomposition" of F: a cell structure with vertex set S, geodesic edges, and 2-cells that are unions of the corresponding Delaunay polygons. Unlike a Delaunay polygon, a centered dual 2-cell Q is not determined by its collection …
Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…
In this paper, we construct Delaunay type constant mean curvature surfaces along a nondegenerate closed geodesic in a 3-dimensional Riemannian manifold.
New matrices link point motions to braid groups.
Study classifies metrics on a twice-punctured sphere, proving Delaunay metrics are complete.
A Delaunay decomposition is a cell decomposition in R^d for which each cell is inscribed in a Euclidean ball which is empty of all other vertices. This article introduces a generalization of the Delaunay decomposition in which the Euclidean balls in the empty ball condition are replaced by other families of regions bou…
We construct constant mean curvature surfaces in euclidean space by gluing n half Delaunay surfaces to a non-degenerate minimal n-noid, using the DPW method.
No compact surfaces with specific curvature can exist near singular limits.
In his seminal 1951 paper "Extreme forms" Coxeter \cite{cox51} observed that for one can add vectors to the perfect lattice $\sfA_9$ so that the resulting perfect lattice, called $\sfA_9^2$ by Coxeter, has exactly the same set of minimal vectors. An inhomogeneous analog of the notion of perfect lattice is tha…
Proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
We use the DPW method to obtain the associate family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential.
New family of trinoids with irregular end found.
Optimal Euclidean structure minimizes energy in weighted toroidal graphs.
New connection found between shape reconstruction methods and persistent homology.
Paper defines and evaluates DR complex for persistent homology.
Constructs special surfaces in hyperbolic space with constant mean curvature.
Four constructions of constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere are given, which should be considered analogues of `classical' constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multipl…
The paper confirms conjectures about the topology of triangulated polyhedra and geodesic triangulations on spheres.
New method constructs surfaces with constant mean curvature.
New method combines DPW and Opening Nodes for positive curvature surfaces.
In this paper we produce families of complete non compact Riemannian metrics with positive constant -curvature by performing the connected sum of a finite number of given -dimensional Delaunay type solutions, provided . The problem is equivalent to solve a second order fully nonlinear elliptic eq…
We give two numerical methods for computing the first bifurcation point for Delaunay nodoids. With regard to methods for constructing constant mean curvature surfaces, we conclude that the bifurcation point in the analytic method of Mazzeo-Pacard is the same as a limiting point encountered in the integrable systems met…
We construct Delaunay-type solutions for the fractional Yamabe problem with an isolated singularity $(-Δ)^γw = c_{n, γ} w^{\frac{n+2γ}{n-2γ}}, w>0 \ \mbox{in} \ \mathbb{R}^n \backslash \{0\}$ We follow a variational approach, in which the key is the computation of the fractional Laplacian in polar coordinates.