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.
Proves equivalence between Koebe circle domain conjecture and Weyl problem for hyperbolic surfaces.
In this paper we parametrize the Teichmüller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of orbifolds determined by certain normal subgroups of their fundamental groups. We also study the covering spaces of the Teichmüller spaces of those Koebe groups. Finally we prove an iso…
Paper extends circle pattern theory to obtuse angles.
We study circle packings with the combinatorics of a triangulated disk in the plane and parametrize deformations of circle packings in terms of vertex rotation and cross ratios. We show that there is a Weierstrass representation formula relating infinitesimal deformations of circle packings to discrete minimal surfaces…
Article explores Thurston's circle packing theorem in 3-manifold geometry.
Historical notes on Thurston's 3-manifold geometry.
New discrete cmc surfaces defined from sphere packings and combinatorics.
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdi`ere's, Br"agger's and Rivin's functionals can be derived fro…
A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin, and that these representatives are unique up to Möbius transformations of the sphere. Motivated by this result, various papers investigate the prob…
We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincaré metrics (i.e., complete metrics of constant negative curvature) by solving the equation on general open surfaces. A few oth…
Unique circle patterns on spheres found for spherical conical metrics.
The Weyl problem is extended to hyperbolic and anti-de Sitter spaces, connecting geometry, analysis, and group theory.
Paper calculates ball number of links using Lorentz geometry and circle packing.
Let $(M, \dr M)$ be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on such that $\dr M$ looks locally like a hyperideal polyhedron, and we characterize the possible dihedral angles. We find as special cases the results of Bao and Bonah…
Survey on uniformization of metric surfaces, including fractal and topological manifolds.
Survey on discrete minimal surfaces and their properties.
New method connects compression bodies through cone manifolds.
Let be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric on such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$ has curvature , and each such metric on $\dr M$ is obtained for a unique ch…
Polyhedra volume conjecture supports Stoker conjecture weakly.
Survey on two non-Kähler geometry conjectures.
Numerical study confirms Brennan's conjecture for a counterexample to Thurston's conjecture.
The non-vanishing conjecture implies the abundance conjecture in certain cases.
Proves Gromov's conjecture and answers Stoker's polyhedron conjecture.
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincare Conjecture. The paper also gives two other algebraic conjectures; one is equi…
Symmetry-breaking in three differential geometry conjectures.
We introduce a new variant of the coarse Baum-Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum-Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum-Connes conjecture. In particula…
Study proves Hecke lifting conjecture for torus knots and verifies it for any framed knots.
New proof shows most thin knots satisfy Cabling Conjecture.
We review the Burghelea conjecture, which constitutes a full computation of the periodic cyclic homology of complex group rings, and its relation to the algebraic Baum-Connes conjecture. The Burghelea conjecture implies the Bass conjecture. We state two conjectures about groups of finite asymptotic dimension, which tog…
Metric SYZ conjecture proved using non-archimedean geometry.
Paper confirms Chen's biharmonic conjecture for hypersurfaces in 5D.
Counterexample disproves recent Penrose conjecture variant.
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
Proof outlined for 4D smooth Poincaré conjecture.
In order to give a unified generalization of the BW inequality and the DDVV inequality, Lu and Wenzel proposed three Conjectures 1, 2, 3 and an open Question 1 in 2016. In this paper we discuss further these conjectures and put forward several new conjectures which will be shown equivalent to Conjecture 2. In particula…
In this paper, we generalize the Cosmetic Surgery Conjecture to an -cusped hyperbolic -manifold and prove it under the assumption of another well-known conjecture in number theory, so called the Zilber-Pink Conjecture. For and , we show them without the assumption.
Paper connects AJ conjecture and colored Jones polynomial potential function.
Akbulut and Kirby conjectured that two knots with the same -surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.
Counterexample disproves conjectures about log canonical thresholds.
Study confirms conjecture on Hermitian manifolds with bounded mass.
Reformulated Markov's conjecture in combinatorial terms.
Paper confirms Whitehead's conjecture for aspherical 2-complexes.
We survey the recent results and current issues on the topological rigidity problem for closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. A number of open problems and conjectures are presented during the course of the discussion. We also review the status and app…
Verifies a conjecture for the figure eight knot.
Fukaya-Yamaguchi conjecture holds in 4D manifolds with nonnegative curvature.
Proved a combinatorial conjecture in machine learning.
In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjec…
There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Propert…