Small entropy self-expanders are topologically unique.
problem Uniqueness of self-expanders with small entropy.
method Analysis of mean curvature flow and cone asymptotics.
result All solutions are in the same isotopy class.
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.
169,051 papers · 148 categories
Trend · papers per month
48 results for “topological uniqueness”
We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA segments. We analyze such experiments for the Mu protein-DNA complex. We characterize t…
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…
Machine learning and topological data analysis identify unique geometric and topological features of human papillae.
problem Identifying unique features of human papillae across individuals.
method 3D microscopic scans, machine learning, discrete differential geometry, computational topology, persistent homology.
result Persistent homology features of papillae shape predict papillae type with high accuracy and can identify individuals with high accuracy.
The study proves the existence and uniqueness of near-horizon geometries for 5D black holes.
problem Existence and uniqueness of near-horizon geometries for 5-dimensional black holes.
method Proved existence and uniqueness of bi-axisymmetric near-horizon geometries with specific topologies and charges.
result Existence and uniqueness of near-horizon geometries for 5D black holes established up to isometry.
This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead the Kirby torus trick. This has the advantage of reducing the point-set topology …
Arguments on PL,(=piecewise linear) topology work over any ordered field in the same way as over the real field, and those on differential topology do over a real closed field R in an o-minimal structure that expands (R,<,0,1,+,cdot). One of the most fundamental properties of definable sets is that a compact definable …
The paper explores how topology affects the solvability of first-order differential equations.
problem The solvability of first-order differential equations and the role of topology.
method Analysis of de Rham cohomology to determine global integrability and uniqueness of solutions.
result Triviality of the first de Rham cohomology group is a fundamental requirement for global integrability and uniqueness of solutions.
Geodesic flows on compact manifolds without conjugate points are shown to have a unique measure of maximal entropy.
problem Analyzing geodesic flows on compact manifolds without conjugate points and with visibility universal covering.
method Using topological mixing, local product structure, and properties of geodesic flows, the authors prove the existence of an expansive factor and uniqueness of measure of maximal entropy.
result The geodesic flow on compact manifolds without conjugate points has a unique measure of maximal entropy.
Two unique conic-line arrangements with degree 9 are found.
problem Identifying Zariski pairs of conic-line arrangements.
method Using connected numbers to distinguish topologies.
result Found two pairs of conic-line arrangements with a unique conic.
AdS uniqueness and black hole energy bounds proven.
problem Proving uniqueness of Anti-de Sitter spacetime and energy bounds for AdS black holes.
method Adapted Wang's proof to static asymptotically locally hyperbolic vacuum metrics and higher-genus horizons.
result Negativity of free energy for AdS black holes with higher-genus horizons.
Paper solves uniqueness of Steklov spectrum on specific manifolds.
problem Determining warping function from Steklov spectrum on hollow sphere manifolds.
method Proves uniqueness of warping function from Steklov spectrum.
result Warping function is uniquely determined by Steklov spectrum.
The Geometry and Topology of Stationary Multi-Axisymmetric Vacuum Black Holes in Higher Dimensionsmath.DG
Proves existence and uniqueness of vacuum black hole solutions in higher dimensions.
problem Existence and uniqueness of solutions to Einstein equations in higher-dimensional spacetimes.
method Develops a generalized plumbing construction and analyzes singular harmonic maps.
result Establishes existence and uniqueness for black hole solutions in -dimensional spacetimes.
HLTF generates chemically valid 3D molecules with improved topology control.
problem Generating chemically valid 3D molecules is challenging due to bond topology errors.
method HLTF uses a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures.
result HLTF achieves high validity and uniqueness on QM9 and GEOM-DRUGS datasets.
Modeling 3D continua with singular points using Yin sets.
problem Treat singular points as central subjects in 3D continuum topology.
method Model 3D continua as Yin sets, regular open semianalytic sets with bounded boundary.
result Characterize local and global topology of Yin sets.
Study reveals failure of uniqueness in dynamical invariants for 3D volume-preserving diffeomorphisms.
problem Uniqueness of dynamical invariants for 3D volume-preserving diffeomorphisms.
method Examined failure of uniqueness on integral homology spheres and arbitrary three-manifolds using local and global invariants.
result Failure of uniqueness is severe, with continuous and non-constant invariants appearing in -open sets of nonvanishing exact fields of fixed helicity.
New framework for 3D spatial topology enumeration and identification.
problem Efficient navigation through complex engineering system topologies.
method Mathematical spatial graph theory to represent, enumerate, and identify unique topological classes.
result Identification of distinctive 3D topological classes for engineering systems.
The paper studies elliptic surfaces and proves unique fibered structures.
problem Understanding the structure of elliptic fibrations and their mapping class groups.
method Analyzes smooth -manifolds and uses Néron-Lang Theorem.
result Proves the uniqueness of fibered structures in elliptic fibrations.
Topological normal generation proved for mapping class groups of certain surfaces.
problem Proving topological normal generation for mapping class groups of surfaces.
method Analyzing the end space of surfaces and using topological normal closure properties.
result Topological normal generation is equivalent to uniquely self-similar for surfaces with countable end space.
The compact-open topology on the homeomorphism group of a surface without boundary is minimalmath.GT
Minimal topology on surface homeomorphisms proven.
problem Proving the compact-open topology is minimal for surface homeomorphisms.
method Combining Hausdorff group topology properties and automatic continuity results.
result Compact-open topology is unique Hausdorff separable group topology on surface homeomorphisms.
Proves uniqueness of certain -symmetric gravitational instantons.
problem Proving uniqueness of -symmetric gravitational instantons.
method Using a divergence identity and results from the -signature theorem.
result Proof of the -symmetric Euclidean Black Hole Uniqueness conjecture.
The paper proves topological finiteness for surfaces with finite Willmore energy.
problem Understanding the topology of surfaces with finite Willmore energy.
method Combining Allard regularity theorem and Reifenberg's topological disk theorem.
result Topological finiteness for a class of properly immersed surfaces with finite Willmore energy.
Infinitely many pairs of free boundary minimal surfaces with the same topology and symmetry groupmath.DG
Researchers found multiple surfaces with same topological and symmetry properties.
problem Determining unique free boundary minimal surfaces from topology and symmetry.
method Provided pairs of non-isometric surfaces with same genus, boundary components, and symmetry group.
result Infinitely many pairs of surfaces with same topology and symmetry group exist.
New metric creates a surface with infinite topology.
problem Constructing a surface with infinite topology.
method Constructing a Riemannian metric and a curve, then finding an area-minimizing surface.
result The area-minimizing surface has infinite topology.
Surface groups are uniquely identified by their profinite completions.
problem Identifying surface groups among limit groups.
method Using profinite completions and topology.
result The set of surface words is closed in the profinite topology.
We use some basic properties of binomial and Stirling numbers to prove that the Euler characteristic is, essentially, the unique numerical topological invariant for compact polyhedra which can be expressed as a linear combination of the numbers of faces of triangulations. We obtain this result converting it into an eig…
Uniqueness proof for Calderón's problem on real-analytic vector bundles.
problem Recovering topology and geometry from boundary measurements of vector bundles.
method Real-analyticity assumption for uniqueness proof.
result Topology and geometry of vector bundles can be recovered from boundary measurements.
Proves existence and uniqueness of solutions for A_n tt*-Toda equations.
problem Existence and uniqueness of solutions for A_n tt*-Toda equations.
method Proof of existence and uniqueness for any n, new treatment of asymptotic data.
result Existence and uniqueness of global solutions for any n.
This research classifies singular foliations and finds a universal deformation.
problem Classifying singular foliations on .
method Topological universal deformation through fixed invariants.
result Every equisingular deformation uniquely factors through the topological universal deformation.
The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space are studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Moebius strips and maximal Klei…
Proves unique symplectic Lefschetz fibration from Morse functions.
problem Mapping Morse functions to symplectic Lefschetz fibrations.
method Homotopically unique complex-valued symplectic Lefschetz fibration on cotangent bundles.
result Existence and uniqueness of symplectic Lefschetz fibrations.
Measuring wave sources uniquely identifies manifold properties.
problem Determining Riemannian manifold structure from wave observations.
method Semilinear wave equation measurements at a single point.
result Topological, differential, and geometric structure can be inferred.
Proves uniqueness of measure of maximal entropy for geodesic flows on surfaces.
problem Proving uniqueness of measure of maximal entropy for geodesic flows on surfaces.
method Analyzes geodesic flows on closed orientable C^∞ surfaces, proving uniqueness of measure of maximal entropy and at most one SRB measure.
result Proves uniqueness of measure of maximal entropy for geodesic flows on surfaces, covering previous results and new examples.
Proves uniqueness of Lefschetz fibrations over discs based on singular fibers.
problem Classifying Lefschetz fibrations over the disc based on their singular fibers.
method Inspired by homological mirror symmetry and Karpov--Nogin's theorem, uses topological equivalence and fiber analysis.
result Lefschetz fibrations over discs are uniquely determined by their singular fibers.
The singly periodic genus-one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature, the celebrated Hoffman-Karcher-Wei's genus one helicoid. The objective of this paper is to give a uniqueness theorem for the singly periodic gen…
We study the number of solutions of the asymptotic Plateau problem in H^3. By using the analytical results in our previous paper, and some topological arguments, we show that there exists an open dense subset of C^3 Jordan curves in S^2_{infty}(H^3) such that any curve in this set bounds a unique least area plane in H^…
The study proves the uniqueness of entropy-maximizing measures for geodesic flows on specific manifolds.
problem Uniqueness of entropy-maximizing measures for geodesic flows on rank 1 manifolds.
method Symbolic dynamics applied to countable topological Markov flows.
result Proof of the uniqueness of the measure of maximal entropy.
In this paper we describe a method to establish when a symplectic manifold with semi-free Hamiltonian -action is unique up to isomorphism (equivariant symplectomorphism). This will rely on a study of the symplectic topology of the reduced spaces. We prove that if the reduced spaces satisfy a rigidity conditi…
Stable solution found for manifold topology from boundary data.
problem Determining manifold properties from boundary data and eigenvalues.
method Quantitative stability estimates and unique continuation for the wave operator.
result Eigenvalues and boundary values determine a metric space close to the manifold.
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spa…
A note on the uniqueness of differential characters and K-theory via homological algebra.
problem Existence and uniqueness of differential characters and differential K-theory.
method Observation and application of Rakesh Pawar's results in homological algebra.
result The hexagon diagram uniquely determines differential K-theory groups up to isomorphism.
The compact-open topology is minimal on diffeomorphism and homeomorphism groups of most smooth manifolds.
problem The minimality of compact-open topology on diffeomorphism and homeomorphism groups.
method Analyzing the compact-open topology on diffeomorphism and homeomorphism groups of smooth manifolds.
result The compact-open topology is minimal on diffeomorphism and homeomorphism groups of most smooth manifolds.
Study finds all possible 5D minimal supergravity solutions with nondegenerate horizons.
problem Finding all possible bi-axially symmetric stationary solutions of 5D minimal supergravity.
method Analyzes the equations for solutions with allowed horizon topologies and asymptotics.
result Identifies the finite number of parameters governing a solution.
New theorem proves uniqueness of Schwarzschild-de Sitter spacetime.
problem Proving the uniqueness of Schwarzschild-de Sitter spacetime.
method Developed new tools like reverse Lojasiewicz inequality and proved smoothness of maximum-set of lapse.
result Established a new uniqueness theorem for three-dimensional Schwarzschild-de Sitter metrics.
Let be a connected non-compact -dimensional manifold possibly with boundary and be a foliation on such that each leaf is homeomorphic to and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. H…
Unique CaTherine wheel found for LQG geodesic tree.
problem Finding a unique CaTherine wheel for LQG geodesic tree.
method Necessary and sufficient conditions for topological trees in .
result Unique CaTherine wheel constructed for LQG geodesic tree.
We give a simple topological argument to show that the number of solutions of the asymptotic Plateau problem in hyperbolic space is generically unique. In particular, we show that the space of codimension-1 closed submanifolds of sphere at infinity, which bounds a unique absolutely area minimizing hypersurface in hyper…
New findings show non-uniqueness in Ricci flow solutions for dimensions n≥5.
problem Non-uniqueness in Ricci flow solutions for dimensions n≥5.
method Exhibited a family of asymptotically conical gradient shrinking solitons with non-unique forward continuations.
result Non-uniqueness of Ricci flow solutions for dimensions n≥5.