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 shows strong multiplicity one property for 3D hyperbolic spaces.
We discuss the geometry of some arithmetic orbifolds locally isometric to a product of real hyperbolic spaces of dimension two and three, and prove that certain sequences of non-uniform orbifolds are convergent to this space in a geometric ("Benjamini--Schramm") sense for hyperbolic three--space and a product of hyperb…
The paper extends carrier graphs to free groups in hyperbolic 3-space.
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.
We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound of the number of exceptional values of them for some topological cases. Moreover, we obtain some new examples for this class.
We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the Ahlfors islands theorem for it and the second one is to give a simple proof of t…
Study Froyshov invariants and closed geodesics in hyperbolic 3-manifolds.
We give the best possible upper bound on the number of exceptional values and the totally ramified value number of the hyperbolic Gauss map for pseudo-algebraic constant mean curvature one surfaces in the hyperbolic three-space and some partial results on the Osserman problem for algebraic case. Moreover, we study the …
We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the -torsion of the universal cover under an additional hypothesis. We also pro…
We explore visual representations of tilings corresponding to Schläfli symbols. In three dimensions, we call these tilings "honeycombs". Schläfli symbols encode, in a very efficient way, regular tilings of spherical, euclidean and hyperbolic spaces in all dimensions. In three dimensions, there are only a finite number …
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.
Characterizes polygonal surfaces in pseudo-hyperbolic spaces.
We analyze the orbifolds that can be obtained as quotients of hyperbolic 3-manifolds admitting a Heegaard splitting of genus two by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the hyperbolic 2-fold branched coverings of 3-bridge links. If the 3-bridge link is a knot, w…
New criteria for relative hyperbolicity in hierarchically hyperbolic spaces.
Following Riemann's idea, we prove the existence of a minimal disk in Euclidean space bounded by three lines in generic position and with three helicoidal ends of angles less than . In the case of general angles, we prove that there exist at most four such minimal disks, we give a sufficient condition of existence i…
The study examines discrete states in hyperbolic spaces using specific transformations.
A soft presentation of hyperbolic spaces, free of differential apparatus, is offered. Fifth Euclid's postulate in such spaces is overthrown and, among other things, it is proved that spheres (equipped with great-circle distances) and hyperbolic and Euclidean spaces are the only locally compact geodesic (i.e., convex) m…
Classifies surfaces in hyperbolic space with constant Gaussian curvature.
The study calculates best Sobolev constants with sharp Hardy terms in Euclidean and hyperbolic spaces.
Paper finds first infinite family of hyperbolic knots with specific properties.
An irreducible 3--manifold with torus boundary either is a Seifert fibered space or admits at most three lens space fillings according to the Cyclic Surgery Theorem. We examine the sharpness of this theorem by classifying the non-hyperbolic manifolds with more than one lens space filling, classifying the hyperbolic man…
New infinite family of hyperbolic L-space knots with specific semigroups.
Constructs hyperbolic reflection groups with 3D limit sets.
Let M be a closed hyperbolic three manifold. We construct closed surfaces which map by immersions into M so that for each one the corresponding mapping on the universal covering spaces is an embedding, or, in other words, the corresponding induced mapping on fundamental groups is an injection.
Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.
Minimal covolume group found in hyperbolic 3-space.
Local X-ray transform works well near boundaries in hyperbolic spaces.
Study complex reflections in infinite Coxeter tetrahedron moduli space.
The goal of this paper is to introduce and study analogues of the Euclidean Funk and Hilbert metrics on open convex subsets of hyperbolic or spherical spaces. At least at a formal level, there are striking similarities among the three cases: Euclidean, spherical and hyperbolic. We start by defining non-Euclidean an…
We investigate surfaces with constant harmonic-mean curvature one (HMC-1 surfaces) in hyperbolic three-space. We allow them to have certain kinds of singularities, and discuss some global properties. As well as flat surfaces and surfaces with constant mean curvature one (CMC-1 surfaces), HMC-1 surfaces belong to a cert…
In this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic balls of three-dimensional hyperbolic space and hemisphere. The pinching condition involves the length of the second fundamental form, the …
Researchers prove Seifert-Weber dodecahedral space is an L-space.
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of these cones. The affine spheres are represented by explicit hypersurface immersions …
Study on discrete complex hyperbolic triangle groups of specific type.
Kashaev's invariants for a knot in a three sphere are generalized to invariants of a knot in a three manifold. A relation between the newly constructed invariants and the hyperbolic volume of the knot complement is observed for some knots in lens spaces.
Examines properties of negatively curved 3-manifolds and their embeddings, introduces Cross Curvature Flow.
The paper sets new limits on hyperbolic polyhedra volumes.
Proves a similar inequality to a conjecture about hyperbolic space hypersurfaces.
New findings on cosmetic surgeries for satellite knots.
The object of study of this article is compact surfaces in the three-dimensional hyperbolic space with a positive-definite second fundamental form. It is shown that several conditions on the Gaussian curvature of the second fundamental form can be satisfied only by extrinsic spheres.
No geometric minimal foliations in hyperbolic 3-manifolds.
Motivated by classical theorems on minimal surface theory in compact hyperbolic three-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic three-manifold of finite volume. We prove any closed immersed incompressible surface can be deform…
The paper generalizes metrics on hyperbolic and anti-de Sitter spaces with curved boundaries.
Sharp bounds derived for eigenvalues on specific geometric spaces.
Study of hyperbolic directions in convex projective geometry.
Paper constructs Hopf real hypersurfaces in complex hyperbolic space.
We list up all the possible local orbit types of hyperbolic or elliptic orbits for the isotropy representations of semisimple pseudo-Riemannian symmetric spaces. It is key to give a recipe to determine the local orbit types of hyperbolic principal orbits by using three kind of restricted root systems and Satake diagram…