Algorithm morphs graphs on hyperbolic surfaces.
problem Morphing graphs on hyperbolic surfaces.
method Generalization of Tutte's spring embedding theorem.
result First algorithm for morphing graphs on hyperbolic surfaces.
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arXiv research
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.
168,742 papers · 148 categories
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For hyperbolic surfaces, primitive lengths are bounded below by a specific formula.
problem Understanding the distribution of primitive closed-geodesic lengths on hyperbolic surfaces.
method Analyzing Teichmüller space and proving a lower bound on the number of distinct primitive lengths.
result There exists a lower bound on the number of distinct primitive closed-geodesic lengths for hyperbolic surfaces.
Exact asymptotic value of Weil-Petersson volumes computed for large genus surfaces.
problem Computing the exact asymptotic value of Weil-Petersson volumes for large genus surfaces.
method Analysis of Witten-Kontsevitch intersection numbers and expansion of volumes.
result Exact asymptotic value of volume polynomials computed for hyperbolic surfaces.
Proofs for spectral and geometric properties of hyperbolic surfaces.
problem Spectral and geometric properties of hyperbolic surfaces.
method Streamlined proofs for isospectral and quasi-Fuchsian groups.
result Generically, isospectral hyperbolic surfaces are isometric.
Lengths of simple closed geodesics on hyperbolic surfaces in prescribed homology classes
problem Estimating the number of simple closed geodesics of a fixed length and homology class on a hyperbolic surface
method Using asymptotic formulas and numerical evidence
result Proving an asymptotic lower bound for the number of such geodesics
Formula for integrating random variables on hyperbolic surfaces.
problem Integrating random variables on the moduli space of hyperbolic surfaces.
method Integration formula for lengths of closed geodesics.
result Integral of geometric random variables can be expressed as an integral over R.
Sharp bound on smallest diameter of hyperbolic surfaces.
problem Finding the smallest possible diameter of hyperbolic surfaces.
method Proved a specific formula for the minimal diameter.
result Minimal diameter is .
The musical notes from a hyperbolic marimba can identify the shape of hyperbolic surfaces.
problem Identifying hyperbolic surfaces based on their musical notes.
method Assigning musical notes to geodesics hitting labeled curves on hyperbolic surfaces.
result The melodies produced by hyperbolic marimbas can characterize hyperbolic surfaces up to isometry.
The entropy of geodesic currents on hyperbolic surfaces is bounded by their self-intersection number.
problem Bounding the entropy of geodesic currents on hyperbolic surfaces.
method Established a quantitative upper bound on entropy in terms of self-intersection number and systole.
result Small self-intersection number forces small entropy.
Geometrically, spherical 3-manifolds emerge from flat SU(2)-bundles over hyperbolic surfaces.
problem Realizing spherical 3-manifolds from flat SU(2)-bundles over hyperbolic surfaces.
method Using Gromov-Hausdorff convergence and systole maximization over moduli spaces.
result Homogeneous spherical 3-manifolds can be realized as limits of metric spaces of flat SU(2)-bundles.
The paper studies the growth of closed geodesics on hyperbolic surface amalgams.
problem Understanding the growth of closed geodesics on hyperbolic surface amalgams.
method Analyzing topological and volume entropies, and their dependence on geometric data.
result Entropy can increase exponentially with pasting length in the absence of a lower bound on the systole.
Recursion formula for the volumes of moduli spaces of compact hyperbolic surfaces with cone pointsmath.GT
Recursion formula derived for moduli spaces of hyperbolic surfaces with cone points.
problem Computing volumes of moduli spaces of hyperbolic surfaces with specific boundary and cone points.
method Using generalized McShane's identities, derived a recursion formula for volumes.
result Obtained a recursion formula for volumes of moduli spaces of hyperbolic surfaces.
Eigenvalues of random hyperbolic surface covers converge to hyperbolic plane's.
problem Eigenvalue rigidity of random hyperbolic surface covers.
method Selberg trace formula and polynomial method.
result Distribution of eigenvalues converges to hyperbolic plane's spectral measure.
The study proves limitations on isospectral hyperbolic surfaces with discrete length spectra.
problem Characterizing isospectral hyperbolic surfaces with discrete length spectra.
method Utilizing Sunada's method and topological self-duplicating ends, the study explores isospectral families and their cardinality.
result Finite groups can be realized as full isometry groups of hyperbolic structures with discrete spectrum on surfaces with self-duplicating ends.
Constructs hyperbolic surfaces with small eigenvalues.
problem Finding hyperbolic surfaces with eigenvalues below a given threshold.
method Geometric proof using techniques from B.Randol's 1974 paper.
result Constructs closed hyperbolic covering surfaces with eigenvalues less than any small positive number ε.
This paper classifies and determines the length of the shortest filling pairs on a specific type of surface.
problem Classifying and determining the length of the shortest filling pairs on a specific type of surface.
method Classifying and determining the length of the shortest filling pairs on a specific type of surface.
result The paper classifies and determines the length of the shortest minimal filling pairs on a genus two surface.
Study Brownian loops on hyperbolic surfaces, linking to Selberg zeta function.
problem Understanding Brownian loops on hyperbolic surfaces and their relation to Selberg zeta function.
method Computed mass of loops and related to Selberg zeta function for geometrically finite surfaces.
result Relate total loop mass to Selberg zeta function, providing probabilistic interpretations of determinants.
Graded identities for hyperbolic surfaces with cusps and cone points.
problem Understanding dilogarithm identities on hyperbolic surfaces.
method Establishing graded versions of Bridgeman's dilogarithm identity.
result Applications to the study of orthogeodesics.
The paper proves a relation between four types of invariants.
problem Proving a precise relation between four types of invariants.
method Analyzing pseudo-Anosov homeomorphisms and cusped hyperbolic 3-manifolds at roots of unity.
result A precise relation between the Baseilhac-Benedetti invariants and the Bonahon-Liu-Wong-Yang invariants.
New bounds on cover degrees for Teichmüller distance between hyperbolic surfaces.
problem Finding optimal cover degrees for Teichmüller distance between hyperbolic surfaces.
method Proved the existence of a constant depending on and such that the covers and can be chosen to have degrees less than .
result The bound is optimal for certain arithmetic Riemann surfaces.
New metric on geodesic currents connects different surface genera.
problem Understanding geodesic currents on surfaces of varying genera.
method Introducing a new asymmetric metric on the space of projective filling geodesic currents.
result Metric spaces of projective filling geodesic currents for surfaces of different genera are not isometric.
The Jacobian of Douady-Earle extension equals 1 only for isometries.
problem Investigating the Jacobian of Douady-Earle extension maps.
method Analyzing the Jacobian of the Douady-Earle extension map and constructing sequences of hyperbolic surfaces.
result The Jacobian of the Douady-Earle extension map is 1 only when the map is an isometry, and it can grow arbitrarily large for certain sequences of surfaces.
Paper extends tree bijection for hyperbolic surfaces without requiring cusps.
problem Computing volumes and distances on hyperbolic surfaces without cusps.
method Extend tree bijection to half-tight cylinders, using Busemann function.
result Tree bijection can now be applied to surfaces without cusps.
Bounding shears in ideal triangulations on hyperbolic surfaces.
problem Bounding shears in ideal triangulations on hyperbolic surfaces.
method Showing an ideal triangulation with bounded shear parameters on hyperbolic surfaces.
result An upper bound on shear parameters depends logarithmically on the surface's topology.
Random covers of surfacesmath.GT
Random covers of hyperbolic surfaces follow a specific probability measure.
problem Understanding the distribution of random covers of hyperbolic surfaces.
method Analyzing random covers subject to specific group isomorphism conditions.
result Asymptotic distribution of random covers according to a probability measure on moduli space of metric graphs.
Improved bounds on shortest geodesics with self-intersections on hyperbolic surfaces.
problem Quantifying the complexity of non-simple closed geodesics on hyperbolic surfaces.
method Analyzing the geometry of shortest figure eight curves and constructing geodesic representatives.
result Explicit upper bounds for the length of shortest geodesics with self-intersections improved from 512 to 128.
New surfaces with special geodesic and horocycle behaviors discovered.
problem Understanding geodesic and horocycle dynamics on hyperbolic surfaces.
method Constructing geometrically infinite hyperbolic surfaces with tailored recurrence properties.
result First examples of non-trivial minimal horocyclic orbit closures and infinite locally-finite conservative horocyclic invariant measures.
The paper studies optimal maps between hyperbolic surfaces, focusing on their rigidity and obstructions.
problem Finding optimal Lipschitz maps between hyperbolic surfaces and understanding their rigidity and obstructions.
method Introducing deflations, optimal maps to trees that obstruct optimal maps between surfaces, and using a smooth orthogeodesic foliation.
result Deflations are the main obstructions to optimal maps between hyperbolic surfaces, and they are essentially the only ones.
The growth rate on the volume of math.GT
The paper calculates the volume growth of hyperbolic surfaces with short geodesics.
problem Understanding the volume growth of hyperbolic surfaces with short geodesics.
method Introduced a function L(g) to measure the length of geodesics and computed the volume growth rate.
result The volume of surfaces with short geodesics is equal to V_g almost surely as g approaches infinity.
Mirzakhani volumes of moduli spaces are polylogarithmic.
problem Understanding the volume of moduli spaces of hyperbolic surfaces.
method Expressed as a sum of polylogarithms evaluated at specific points.
result Mirzakhani volumes are polylogarithmic.
Paper disproves Wright's periodic map conjecture.
problem Existence of periodic maps on closed hyperbolic surfaces.
method Analyzes automorphisms and curve behavior on surfaces.
result No periodic map can fill every curve with its image.
The paper studies the shortest closed multi-geodesics on hyperbolic surfaces as their genus grows.
problem Finding the asymptotic behavior of shortest closed multi-geodesics on hyperbolic surfaces.
method Analyzing the length of shortest filling closed multi-geodesics using hyperbolic geometry and asymptotic analysis.
result The length of a shortest filling closed multi-geodesic is uniformly comparable to a specific formula involving the genus and lengths of closed geodesics.