Quantum bundles use metrics to measure distances.
problem Measuring distances on quantum spaces.
method Using Riemannian metrics and Rosenberg's Levi-Civita connections.
result Distance between bundles from positive scalar metrics is zero.
On-device research index
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.
169,291 papers · 148 categories
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48 results for “Modular Gromov-Hausdorff propinquity”
The paper proves stability in compact finite dimensional Alexandrov spaces using equivariant Gromov--Hausdorff convergence.
problem Stability in compact finite dimensional Alexandrov spaces.
method Equivariant Gromov--Hausdorff convergence and almost commutative diagrams.
result Stability result in compact finite dimensional Alexandrov spaces.
Study Gromov-Hausdorff convergence of metric pairs and tuples.
problem Understanding convergence in metric spaces.
method Prove equivalence of definitions, embedding, completeness, and compactness theorems.
result Relative version of Fukaya's theorem and finiteness theorem for stratified spaces.
Study on curved spheres' topology.
problem Topology of curved spheres.
method Gromov-Hausdorff metric on isometry classes.
result Properties of curved spheres' metric space.
Study describes limits of surfaces in a mathematical space.
problem Understanding limits of surfaces in mathematical spaces.
method Completely described Gromov-Hausdorff closure of surfaces.
result Completely described the closure of surfaces.
Study uses equivariant topology to measure distances between G metric spaces.
problem Measuring distances between G metric spaces.
method Equivariant topology methods to derive lower bounds.
result Sharp bounds on Gromov Hausdorff distance between spheres.
Polynomial algorithm estimates mGH distance between unweighted graphs.
problem Efficiently measuring shape difference between unweighted graphs.
method Polynomial algorithm for mGH distance estimation.
result Algorithm finds mGH distances exactly on most scale-free graphs.
Study shows intrinsic timed Hausdorff convergence leads to Gromov-Hausdorff and big bang convergence.
problem Distance between Lorentzian manifolds.
method Intrinsic timed Hausdorff convergence.
result Intrinsic timed Hausdorff convergence implies Gromov-Hausdorff and big bang convergence.
Paper calculates Gromov-Hausdorff distance between simplexes and 2-distance spaces.
problem Calculating Gromov-Hausdorff distance between simplexes and 2-distance spaces.
method Formulas derived for clique covering number and chromatic number of graphs.
result Complete solution to generalized Borsuk problem for 2-distance spaces.
Stability of Wasserstein spaces under various convergence types.
problem Stability and finiteness of Wasserstein spaces over singular and non-singular spaces.
method Gromov--Hausdorff convergence and equivariant Gromov--Hausdorff convergence.
result Analogue of Perelman's stability theorem on Wasserstein spaces.
Polynomial-time relaxation improves Gromov-Hausdorff metric computation.
problem Computing Gromov-Hausdorff distance is intractable.
method Semidefinite programming relaxation of Gromov-Hausdorff metric.
result Relaxed distance can be computed in polynomial time.
New theorem on flat tori stability using harmonic maps and Ricci flow.
problem Stability of flat tori under Ricci and scalar curvature bounds.
method Harmonic map heat flow, Ricci flow, and RCD theories.
result Gromov-Hausdorff stability theorem for flat 3-tori.
The paper connects geometric and topological concepts to bound distances between metric spaces.
problem Bounding distances between metric spaces using Gromov-Hausdorff distance.
method Using Borsuk-Ulam theorems and Vietoris-Rips complexes, the paper obstructs the existence of certain continuous maps between complexes to bound discontinuities of functions.
result The paper provides new bounds on Gromov-Hausdorff distances between spheres of different dimensions.
The paper constructs metrics on tori with Ricci bounds and shows Gromov-Hausdorff limits are not always manifolds.
problem Understanding the Gromov-Hausdorff limits of tori with Ricci conditions.
method Constructing metrics on and analyzing their limits.
result The Gromov-Hausdorff limit of tori with Ricci bounds is not always a topological manifold.
Flow analysis leads to metric completion in Kähler geometry.
problem Analyzing Kähler-Ricci flows on compact manifolds.
method Normalized Kähler-Ricci flow convergence to Gromov-Hausdorff limits.
result Metric completion of twisted Kähler-Einstein metric.
Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen typemath.AG
Study Gromov-Hausdorff limits of K3 surface metrics via moduli compactification.
problem Understanding limits of K3 surface metrics.
method Moduli-theoretic framework for collapsing Ricci-flat Kahler metrics.
result Gromov-Hausdorff limits of hyperKahler metrics with fixed diameters.
This paper introduces a new distance metric for filtered A-infinity categories, focusing on Lagrangian submanifolds.
problem Measuring the distance between filtered A-infinity categories associated with Lagrangian submanifolds.
method Developed a Gromov-Hausdorff distance to measure the difference between these categories.
result Established that the sequence of filtered A-infinity categories forms a Cauchy sequence in Gromov-Hausdorff distance.
Study shows continuity of non-Kähler Calabi-Yau conifold transitions.
problem Understanding the geometry of Calabi-Yau conifold transitions.
method Use of balanced and Hermitian-Yang-Mills metrics to analyze conifold transitions.
result The conifold transition is continuous in the Gromov-Hausdorff topology.
Study on metric spaces with properties (ETR), (LBD) and their convergence.
problem Understanding orientability and convergence of metric measure spaces.
method Analysis of Gromov-Hausdorff and intrinsic flat convergence for spaces satisfying (ETR), (LBD).
result The pointed Gromov-Hausdorff limit coincides with the local flat limit.
New method uses cohomology to quantify molecular similarity.
problem Quantifying structural dissimilarity in molecular data.
method Gromov-Hausdorff ultrametric based on simplicial complexes and cohomology.
result Demonstrates effectiveness in clustering organic-inorganic halide perovskite structures.
Compactifies metrics on K3 surfaces with algebraic description.
problem Classify Gromov-Hausdorff limits of K3 surfaces with fixed structures or polarizations.
method Algebraic description of Gromov-Hausdorff compactification.
result Classification of Gromov-Hausdorff limits of K3 surfaces.
The paper explores null distance convergence for warped product spacetimes.
problem Defining convergence for sequences of spacetimes as metric spaces.
method Using the null distance to define convergence of spacetimes.
result Optimal convergence theorem for warped product spacetimes.
Study limits of Kähler manifolds with bounded Ricci curvature.
problem Understanding the structure of limits of Kähler manifolds.
method Analysis of Gromov-Hausdorff limits with Ricci curvature bounds.
result Each tangent cone is homeomorphic to a normal affine variety.
Study of Calabi-Yau metrics on converging manifolds, resolving conjectures.
problem Understanding Calabi-Yau metrics on converging manifolds.
method Analysis of Gromov-Hausdorff limits of metrics on Calabi-Yau fibrations.
result Gromov-Hausdorff limit is homeomorphic to the base of the fibration and discriminant locus has high Hausdorff codimension.
We discuss the behavior of with respect to the Gromov-Hausdorff topology and the variable , where is the first positive eigenvalue of the -Laplacian on a compact Riemannian manifold . Applications include new estimates for the first eigenvalues of the -Laplacian on Rieman…
The paper proves isoperimetric regions on Riemannian manifolds with Ricci bounded below.
problem Proving the existence of isoperimetric regions in Riemannian manifolds.
method Gromov-Hausdorff asymptotic analysis to study perimeter-minimizing sequences.
result Existence of isoperimetric regions in noncollapsed Riemannian manifolds with Ricci curvature bound.
We investigate compact Hausdorff foliations on compact Riemannian manifolds in the context of the Gromov-Hausdorff distance theory. We give some sufficient conditions for such foliations to be separated in the Gromov-Hausdorff topology.
The paper examines conditions for Gromov-Hausdorff convergence of metric quotients and provides examples of conic-flat surfaces.
problem Conditions for Gromov-Hausdorff convergence of metric quotients.
method Analyzes sufficient conditions for Gromov-Hausdorff convergence of metric quotients of a metric space.
result Concrete examples of sequences of two-dimensional conic-flat spheres converging to spheres with singularities.
The paper constructs Gromov-Hausdorff metrics for Lorentzian spaces and calculates dimensions.
problem Understanding the geometry and dimensions of Lorentzian spaces.
method Construction of Gromov-Hausdorff metrics, calculation of dimensions, and analysis of Lorentzian spaces.
result Dushnik-Miller dimension of Minkowski spaces is countably infinite.
In this paper we continue to study Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Our main focus is on the algebro-geometric meaning of Riemannian tangent cones and rescaled limits.
Circle's metric is at least π/4 away from any simply connected geodesic space.
problem Comparing simply connected geodesic spaces to the circle.
method Using Gromov-Hausdorff distance and topological properties.
result The Gromov-Hausdorff distance between circle and any simply connected geodesic space is at least π/4.
Study G-H limits of surfaces with boundary, focusing on same Euler characteristic.
problem Investigate Gromov-Hausdorff limits of compact surfaces with boundary.
method Focus on surfaces with same Euler characteristic, build on previous work on closed surfaces.
result Complete description and topological properties of limit spaces.
Proves Einstein metrics close to orbifolds are gluing of model spaces.
problem Can Einstein orbifolds be limits of smooth Einstein manifolds?
method Controlled metric convergence in neck regions using optimal coordinates.
result Einstein metrics close to orbifolds are gluing of model spaces.
We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely Gromov-Hausdorff. Corollaries include Reeb's local stability theor…
Magnitude is not continuous but may be stable for most finite metric spaces.
problem Stability of magnitude invariant in finite metric spaces.
method Investigates the continuity properties of magnitude with respect to Gromov-Hausdorff topology.
result Magnitude is nowhere continuous but may be generically continuous.
We develop a new approach to, and small extension of, results of Cheeger, Colding and Tian concerning the norm of the curvature of a Riemannian manifold Gromov-Hausdorff close to a codimension singularity.
Intrinsic flat and Gromov-Hausdorff convergence of manifolds with Ricci curvature bounded belowmath.DG
We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature uniformly bounded from below and diameter uniformly bounded above, Gromov-Hausdorff convergence essentially agrees with intrinsic flat convergence.
Gromov-Hausdorff-like distance function defined in the aspect of Riemannian submanifold theorymath.DG
Defines a Gromov-Hausdorff-like distance for Riemannian manifolds.
problem Defining a distance function for isometric classes of compact Riemannian manifolds.
method Using the Hausdorff distance function in the tangent bundle with the Sasaki metric.
result The convergence of a sequence of compact Riemannian manifolds coincides with the R. S. Hamilton convergence.
New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded belowmath.DG
This paper constructs a function on Gromov-Hausdorff limits of 2-surfaces with curvature constraints.
problem Understanding geometric properties of limits of surfaces with curvature constraints.
method Construction of an integer-valued function on the limit space.
result Existence and classification of functions on Gromov-Hausdorff limits of 2-surfaces.
We give the definition of -convergence of tensor fields with respect to the Gromov-Hausdorff topology and several fundamental properties of the convergence. We apply this to establish a Bochner-type inequality which keeps the term of Hessian on the Gromov-Hausdorff limit space of a sequence of Riemannian manifolds…
Bounds and constructions for Gromov-Hausdorff distance between spheres.
problem Calculating distances between spheres using Gromov-Hausdorff metric.
method Explicit constructions and topological ideas based on Borsuk-Ulam theorem.
result Lower bounds are tight for specific cases of sphere distances.
An older paper by Edwards introduced the Gromov-Hausdorff distance.
problem Determining the first inventor of the Gromov-Hausdorff distance.
method Comparing metric spaces through isometric embeddings and measuring Hausdorff distance.
result David Edwards published the Gromov-Hausdorff distance 6 years before M. Gromov.
Newly discovered Eguchi-Hanson metric arises from edge metrics.
problem Understanding limits of compact singular Einstein spaces.
method Constructing Kahler-Einstein edge metrics on Calabi-Hirzebruch manifolds.
result Eguchi-Hanson metric emerges as a Gromov-Hausdorff limit.
Topology of non-orientable spaces without boundary is studied.
problem Topology of non-collapsed RCD spaces without boundary.
method Studied the stability of non-orientability and topology under Gromov-Hausdorff convergence.
result Non-orientable spaces without boundary have a stable ramified double cover.
Paper uses Gromov-Hausdorff convergence to re-examine surface classification.
problem Classifying complete Riemannian surfaces with finite total curvature.
method Gromov-Hausdorff convergence theory applied to surfaces.
result New understanding of Huber's classification theorem for surfaces.
Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
problem Stability of the Schwarzschild 3-manifold in the context of the 3D Riemannian Penrose inequality.
method Pointed measured Gromov-Hausdorff topology, negligible domains and boundary area perturbations.
result Schwarzschild 3-manifold stability proven for 3D Penrose inequality.
3d Modularityhep-th
Discoveries new symmetries in 3d topological and physical systems.
problem Identifying hidden symmetries in 3d topological and physical systems.
method Analysis of modular forms, Weil representations, and chiral algebras.
result Identification of new modular structures in 3d theories.
Study shows properties of Gromov-Hausdorff limit of frame bundles for non-collapsed manifolds.
problem Characterizing the Gromov-Hausdorff limit of orthonormal frame bundles of non-collapsed manifolds with bounded Ricci curvature.
method Analysis of the Gromov-Hausdorff limit space of orthonormal frame bundles equipped with an almost canonical metric.
result The singular set of the limit space has codimension and the complement contains an open and dense -Riemannian manifold.