Berestovskii and Plaut introduced the concept of a coverable uniform space when developing their theory of generalized universal covering maps for uniform spaces. Brodskiy, Dydak, LaBuz, and Mitra introduced the concept of a locally uniformly joinable uniform space when developing their theory of generalized uniform co…
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48 results for “uniform spaces”
This paper refines homotopy theory for cubical sets and uniform spaces.
problem Classical homotopy theory limitations in cubical sets and uniform spaces.
method Develops a uniform-theoretic refinement for cubical sets and uniform spaces, lifting to a full and faithful embedding.
result Lifts classical homotopy categories to new uniform homotopy categories, generalizing cohomology theories.
Metrizable uniform spacesmath.GT
Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results include: 1) If f: A -> Y is a uniformly continuous map, where X and Y are metric spac…
Generalizes uniformization to algebraic correspondences.
problem Uniformizing non-homeomorphic genus zero orbifolds.
method Constructs algebraic correspondences to simultaneously uniformize orbifolds.
result Realizes Teichmüller space of a punctured sphere in correspondences.
In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local contractibility of the group of uniform homeomorphisms of such a metric covering space under t…
In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given…
Uniform Poincaré inequalities established for various metric spaces.
problem Establishing uniform Poincaré inequalities on different metric spaces.
method Proper geodesic metric spaces equipped with a Borel measure. Local Poincaré inequality and volume conditions are used to derive uniform Poincaré inequalities.
result Uniform Poincaré inequalities are established for various metric spaces including hyperbolic spaces and covers of compact spaces.
The uniform structure on a differential space defined by a family of generators is considered.
The paper explores uniform perfectness and centers in Morse boundaries.
problem Detecting -center exhaustivity in uniformly perfect Morse boundaries.
method Analyzes CAT(0) and geodesic spaces, using visual boundary data and metric transforms.
result Fixed-basepoint uniform perfectness is insufficient for -center exhaustivity.
Uniformizes compact Sasakian manifolds into circle bundles.
problem Deforming compact Sasakian manifolds to locally isomorphic forms.
method Criterion based on circle bundles of anti-canonical bundles over Hermitian symmetric spaces.
result Sasakian manifolds can be deformed to locally isomorphic forms.
A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…
Uniform bounds on ends for non-branching CD spaces with nonnegative curvature outside a compact set.
problem Bounding the number of ends of non-branching CD spaces with nonnegative curvature outside a compact set.
method Adapting Z.-D. Liu's work to prove a ball covering property.
result Uniform bounds on the number of ends of such spaces.
New proof of uniformization for hyperbolic foliations.
problem Uniformization of foliated spaces by surfaces of hyperbolic type.
method Laminated Ricci flow to find a conformally equivalent metric with constant curvature -1.
result Existence of a laminated Riemannian metric with leaves of constant Gaussian curvature -1.
In the product space H^n \times R; we obtain uniform a priori C^0 horizontal length estimates, uniform a priori C^1 boundary gradient estimates, as well as uniform modulus of continuity, for a class of horizontal minimal equations. In two independent variables, we derive a certain uniform global a priori C^1 estimates …
Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metricmath.DS
The paper studies Blaschke products, proving uniformization and non-degeneracy of pressure metrics.
problem Analytic aspects of Blaschke products and their moduli space.
method Definition of complex structure and proof of uniformization theorem.
result Pressure semi-norms are non-degenerate outside the super-attracting locus.
Uniform convexity in divisible domains leads to hyperbolic geometry.
problem Understanding the geometry of divisible convex sets in Finsler manifolds.
method Proving -uniform convexity of a specific Finsler metric.
result A strictly convex divisible domain induces a -uniformly convex Finsler metric.
The parametrization theorem is derived in a flat nD pseudo-complex affine space. The pseudo-complex hyperbolic space accomodates n-number of uncompactified time-like extra dimensions with sugnature (s,r), where s and r are the numbers of minus and plus signs associated with the diagonalized metric matrix. The main resu…
Uniform covers with a finite-dimensional nerve are rare (i.e., do not form a cofinal family) in many separable metric spaces of interest. To get hold on uniform homotopy properties of these spaces, a reasonably behaved notion of an infinite-dimensional metric polyhedron is needed; a specific list of desired properties …
Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie algebras and we classify uniform Lie algebras with five or fewer generators. We defi…
Study proves uniform ellipticity implies uniform polyconvexity for anisotropic energy functionals.
problem Investigating uniform ellipticity and polyconvexity for anisotropic geometric energy functionals.
method Proves a variant of a recent result using real polyhedral chains.
result Uniform ellipticity of an anisotropic energy functional implies uniform polyconvexity of the integrand.
Survey on uniformization of metric surfaces, including fractal and topological manifolds.
problem Uniformization of metric surfaces homeomorphic to 2D topological manifolds.
method Various uniformization theorems, including quasisymmetric and quasiconformal approaches.
result Uniformization results for metric spheres and arbitrary metric surfaces.
The paper develops a uniform function estimator in RKHS for regression.
problem Reconstructing functions from noisy data at random locations.
method Using reproducing kernel Hilbert spaces and Gaussian random fields.
result The estimator converges uniformly to the conditional expectation.
Uniform entropy bound for Ricci shrinkers with bounded curvature.
problem Bounding entropy for Ricci shrinkers with specific curvature constraints.
method Establishing uniform entropy bounds for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
result Uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and uniform curvature bounds.
Let S be a compact connected oriented orbifold surface We show that using Bers simultaneous uniformization, the moduli space of projective structure on S can be mapped biholomorphically onto the total space of the holomorphic cotangent bundle of the Teichmüller space for S. The total space of the holomorphic cotangent …
Uniformizes compact complex manifolds via Anosov representations.
problem Uniformization of compact complex manifolds.
method Anosov homomorphisms with small limit sets.
result Local homeomorphism of character variety to Teichmüller space.
We prove that if is the Gromov-Hausdorff limit of a sequence of compact manifolds, , with a uniform lower bound on Ricci curvature and a uniform upper bound on diameter, then has a universal cover. We then show that, for sufficiently large, the fundamental group of has a surjective homeomorphis…
In this article we show that for every finite area hyperbolic surface of type and any harmonic Beltrami differential on , then the magnitude of at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil-Petersson norm of over the square root of the systole…
We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be characterized with parallel constructions using a combinatoric tool called common zi…
The study examines metrics on Riemannian spaces with bounded properties and finds conditions for Lipschitz and uniform bounds.
problem Investigating bounded rough Riemannian metrics and their properties.
method Analyzing the structure of bounded rough Riemannian metrics and finding conditions for Lipschitz and uniform bounds.
result Weak conditions are identified for Lipschitz and uniform bounds on the metrics.
Geometric interpretation of Fock-Goncharov positivity and disk stabilization in symmetric space.
problem Understanding Fock-Goncharov positivity and its geometric implications.
method Geometric interpretation and bending deformations of Fuchsian representations.
result Stabilization of a uniform Finsler quasi-convex disk in the symmetric space.
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature Kähler metrics. We carry this out by exploring in detail the metric geometry of Mabuchi geodesic rays, and the uniform convexity properties of the space of Kähler metrics.
New approach finds minima of geodesic lengths for non-uniform fillings.
problem Finding minima of geodesic length functions for non-uniform fillings.
method Elementary optimization for 4-regular topological fillings, analysis of fat graphs and optimization techniques.
result Minima of geodesic length functions are found to be at triangle surfaces in both analyzed classes of non-uniform fillings.
The paper establishes a uniform Lipschitz bound on the square root of the systole function in Teichmüller space.
problem Uniform Lipschitz bounds on geometric functions in Teichmüller space.
method Injectivity radius analysis and Lipschitz bounds on systole function.
result Uniform Lipschitz constant for the square root of the systole function on Teichmüller space.
We give several sufficient conditions for uniform exponential growth in the setting of virtually torsion-free hierarchically hyperbolic groups. For example, any hierarchically hyperbolic group that is also acylindrically hyperbolic has uniform exponential growth. In addition, we provide a quasi-isometric characterizati…
Online learning of linear operators between infinite-dimensional spaces is possible but with limitations.
problem Learning linear operators between infinite-dimensional Hilbert spaces in an online setting.
method Online learning approach for linear operators with bounded -Schatten norm, proving impossibility for operator norm.
result Separation between online learnability and uniform convergence for bounded linear operators.
Uniform elliptic theory for Dirac operators on orbifold resolutions.
problem Analyzing Dirac operators on orbifold resolutions.
method Viewing orbifolds as conically fibred singular spaces and resolving them by gluing asymptotically conical fibrations.
result Uniform index formula for Dirac operators on orbifold resolutions.
We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. This generalization will follow as a corollary from a local index theorem that is valid on any manifold of bounded geometry. This local formula incorporates the un…
Uniform proof reconstructs spaces using cross ratio on boundary.
problem Reconstructing spaces using cross ratio on boundary.
method Using CAT(-1) spaces and cross ratio on visual boundary.
result Spaces can be reconstructed using cross ratio on boundary.
The uniform boundary condition in a normed chain complex asks for a uniform linear bound on fillings of null-homologous cycles. For the -norm on the singular chain complex, Matsumoto and Morita established a characterisation of the uniform boundary condition in terms of bounded cohomology. In particular, spaces…
Uniform estimates for elliptic problems near polygonal domains.
problem Proving uniform solvability estimates for elliptic problems near polygonal domains.
method Suitable conformal modification of the metric to make the union of domains a manifold with boundary and relative bounded geometry.
result Rounding off the corners of the limit polygonal domain.
Uniform convergence of metrics on vortex moduli space in Bradlow limit.
problem Understanding the geometry of vortex moduli spaces.
method Proof of uniform convergence of metrics using normalized metric and Fubini-Study metric.
result Establishes the Fubini-Study metric as the limit of the normalized metric in the Bradlow limit.
In this note, we study deformations of a non-uniform real hyperbolic lattice in quaternionic hyperbolic spaces. Specially we show that the representations of the fundamental group of the figure eight knot complement into PU(2,1) cannot be deformed in out of PU(2,1) up to conjugacy.
Uniform linear bounds on volume changes in 3D hyperbolic spaces.
problem Volume variation in hyperbolic 3-manifolds.
method Uniform linear bounds proof for drilling and filling operations.
result Uniform linear bounds on volume variation proved.
We prove effective uniformization for nearly round 2-spheres and investigate their stability.
problem Proving effective uniformization for nearly round 2-spheres and their stability.
method Utilizing an identity related to the third-order differential of the conformal factor, and an isometric embedding of a round sphere into Euclidean space using an orthogonal basis of the first eigenspace of the Laplacian operator.
result We provide a simplified proof of effective uniformization and its stability.
Study defines new products for Lorentzian spaces and analyzes causal diamonds.
problem Understanding causal diamonds in Lorentzian spaces.
method Introduced taxicab and uniform products for Lorentzian pre-length spaces. Defined space and analyzed its properties.
result The space is geodesic and globally hyperbolic for complete .
We prove a uniform estimate, valid for every closed Riemann surface of genus at least two, that bounds the distance of any quadratic differential to the finite dimensional space of holomorphic quadratic differentials in terms of its antiholomorphic derivative.
Study shows how non-uniform scaling affects persistence diagrams.
problem Stability of persistence diagrams under non-uniform scaling.
method Explicit bounds on bottleneck distance derived for Euclidean scaling.
result Explicit bounds on the stability of persistence diagrams under non-uniform scaling.