Proves existence of Yamabe metrics on conical manifolds with conical points and links.
problem Existence of Yamabe metrics on singular manifolds with conical points and links.
method Derives a counterpart of Aubin's result, uses conical links and Fourier analysis, adds lower-order correction to standard bubbles.
result Derives asymptotic expansions on the Yamabe quotient for generic type metrics.
Link condition for simplicial complexes to be CUB spaces.
problem Understanding when a simplicial complex is a CUB space.
method Establishing a link condition based on local lattice properties.
result The link condition generalizes Gromov's link condition for cube complexes.
Introduces new Hermitian metrics linking to Gauduchon and balanced metrics.
problem Finding conditions for compact complex manifolds to be Kähler.
method Introducing pluriclosed star split metrics and studying their properties.
result Affirmative answer to Fino-Vezzoni conjecture under extra assumptions.
The paper connects 3D manifold invariants to hyperbolic cone metrics and discrete Fourier transforms.
problem Volume conjecture for Reshetikhin-Turaev invariants of 3-manifolds with links.
method Volume conjecture, hyperbolic cone metrics, discrete Fourier transforms, change-of-pair operations.
result Volume conjecture proven for specific cases, provides approach to solving Volume Conjecture for hyperbolic 3-manifolds.
Study on new metrics on para-Kähler-Norden manifolds with conformal deformation.
problem Exploring geometric and harmonic properties of new metrics.
method Conformal deformation of Berger-type metric, analysis of Levi-Civita link, study of curvature varieties, and harmonic maps.
result Detailed examination of curvature varieties and harmonic maps on the manifold.
The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot t(2n+1,2) or the torus link t(2n,2). Domains of existence for a spherical metric are found in terms of cone angles and volume formulæ are presented.
Study identifies Kähler-Einstein, Kähler-Ricci soliton, and Sasaki-Einstein metrics on log del Pezzo surfaces.
problem Characterizing log del Pezzo surfaces with specific geometric properties.
method Examining two classes of non-toric log del Pezzo surfaces and analyzing their geometric properties.
result Examples found that admit Kähler-Ricci solitons but not Sasaki-Einstein cone links.
Paper shows pseudometrics on braid groups are nondegenerate.
problem Stability of braid types defined by symplectic morphisms.
method Uses Hofer metric to define pseudometrics and shows stability under small distance.
result Pseudometrics are nondegenerate.
Study finds conditions for conformal deformations to constant scalar curvature in conic metrics.
problem Finding conditions for conformal deformations to constant scalar curvature in conic metrics.
method Analyzes conformal deformations within a class of incomplete Riemannian metrics that generalize conic orbifold singularities.
result Determines sufficient conditions for the existence of a conformal deformation to a conic metric with constant scalar curvature -1.
Road Network Metric Learning improves ETA prediction accuracy by addressing data sparsity.
problem Data sparsity in road network embedding vectors affects ETA prediction accuracy.
method Proposes Road Network Metric Learning (RNML-ETA) framework with an auxiliary metric learning task and triangle loss.
result RNML-ETA outperforms state-of-the-art models and improves prediction accuracy for cold links.
Predicting the future evolution of complex systems is one of the main challenges in complexity science. Based on a current snapshot of a network, link prediction algorithms aim to predict its future evolution. We apply here link prediction algorithms to data on the international trade between countries. This data can b…
Positive scalar curvature metrics on cobordisms yield only reducible Seiberg-Witten solutions.
problem Counting solutions to Seiberg-Witten equations on cobordisms.
method Constructing families of metrics with positive scalar curvature.
result Irreducible solutions are absent when positive scalar curvature metrics are used.
Most of metric learning approaches are dedicated to be applied on data described by feature vectors, with some notable exceptions such as times series, trees or graphs. The objective of this paper is to propose a metric learning algorithm that specifically considers relational data. The proposed approach can take benef…
Lower bound found for volumes of modular link complements.
problem Finding a lower bound for the volumes of modular link complements.
method Analyzing the volumes of link complements associated with geodesics in the modular surface.
result First linear lower volume bound in terms of exponents of code words.
From a hermitian metric on the anticanonical bundle on a Del Pezzo surface, and a holomorphic section of it, we construct a one parameter family of bihermitian metrics (or equivalently generalized Kaehler structures). The construction appears to be linked to noncommutative geometry.
New methods link Calabi-Yau metrics to random matrices.
problem Lack of explicit metrics on Calabi-Yau manifolds hinders particle physics computations.
method Numerical approximations of the Laplacian spectrum on Calabi-Yau spaces.
result Surprising link found between Calabi-Yau metrics and random matrix theory.
Framework analyzes physical metrics in soccer to link performance with value.
problem Understanding and quantifying the value of physical performance in soccer.
method Estimating physical indicators from tracking data, contextualizing runs, linking with possession-value model.
result Physical performance correlates with value generation in soccer.
The paper discusses polynomial convergence to conical Kähler-Einstein metrics.
problem Understanding the convergence of Kähler-Einstein metrics to conical structures.
method Two-step degeneration theory and algebraic singularity analysis.
result Singular Kähler-Einstein metrics are conical if curvature grows quadratically near a point.
Study local moduli of Sasaki-Einstein metrics on specific polynomial links.
problem Understanding the local moduli of Sasaki-Einstein metrics on links of invertible polynomials.
method Analyzing Sasaki-Einstein metrics on links of invertible polynomials of cycle type and Thom-Sebastiani sums.
result For polynomials of cycle type, local moduli spaces are zero-dimensional. For Thom-Sebastiani sums, dimensions are positive.
New examples of Calabi-Yau metrics on cones with irregular smooth links.
problem Finding new Calabi-Yau metrics on cones with irregular smooth links.
method Explicit computation of Reeb field and Minkowski decompositions of toric Calabi-Yau cones.
result Examples of complete Calabi-Yau metrics on cones with irregular smooth links.
We inspect Vietoris-Rips complexes VRt(X) of certain metric spaces X using a new generalization of Bestvina-Brady discrete Morse theory. Our main result is a pair of metric criteria on X, called the Morse Criterion and Link Criterion, that allow us to deduce information about the homotopy types of certain $VR_t(…
New metrics defined on SPD matrices link to divergences and curvature.
problem Defining and characterizing metrics on SPD matrices.
method Developed a principle of deformed metrics and introduced balanced bilinear forms.
result Introduce Mixed-Euclidean metrics with negative sectional curvature.
In this work we study the intrinsic geometry of the space of Kahler metrics under various Riemannian metrics. The first part is on the Dirichlet metric. We motivate its study, we compute its curvature, and we make links with the Calabi metric, the K-energy, the degenerate complex Hessian equation. The second part is on…
A link of an isolated singularity of a two-dimensional semialgebraic surface in R4 is a knot (or a link) in S3. Thus the ambient Lipschitz classification of surface singularities in R4 can be interpreted as a bi-Lipschitz refinement of the topological classification of knots (or links) in S3. We show that, …
SELO model predicts link signs better than SDGNN using subgraph encoding and linear optimization.
problem Inferring the sign of links in signed networks with limited sign data.
method Subgraph Encoding via Linear Optimization (SELO) approach to learn edge embeddings.
result SELO model outperforms state-of-the-art methods on multiple real-world signed networks.
We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian structures occuring on links of isolated hypersurface singularities.
New bounds improve linkage methods for clustering, distinguishing complete-link from single-link.
problem Improving bounds on linkage methods for clustering quality.
method Developed new bounds for complete-link and average-link methods in agglomeration clustering.
result Separated complete-link from single-link in terms of approximation for diameter.
Following the Euclidean results of Varopoulos and Pankka--Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold M to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group H. As an application, we show that a link complement S3\L has a …
Hermitian-Einstein metrics linked to stability of bundles on orbifolds.
problem Existence of Hermitian-Einstein metrics on stable vector bundles over compact Kähler orbifolds.
method Equivalence of slope stability to the existence of Hermitian-Einstein metrics and properness of a functional.
result Equivalence of Hermitian-Einstein metrics and slope stability for stable vector bundles.
Starfield optimizes satellite links for LEO mega-constellations by aligning ISLs with regional traffic patterns.
problem Forming a stable satellite topology in LEO mega-constellations with limited ISLs and unstable acquisition.
method Starfield uses a demand-aware heuristic algorithm based on traffic flows and Riemannian geometry to assign satellite links.
result Starfield reduces hop count and improves stretch factor by up to 30% compared to existing methods.
Develops symmetric Cartan calculus linking to Patterson-Walker metric.
problem No specific problem stated; focuses on developing a new calculus.
method Symmetric Cartan calculus, using torsion-free affine connections.
result Symmetric Cartan calculus is a complete analogue of classical Cartan calculus.
Counterexample disproves conjecture on flat metrics and fiber bundles.
problem Conjecture about flat metrics and fiber bundles on manifolds.
method Study of transversely flat Riemannian foliations.
result Found a counterexample to the conjecture.
We construct a spectral sequence from the reduced odd Khovanov homology of a link converging to the framed instanton homology of the double cover branched over the link, with orientation reversed. Framed instanton homology counts certain instantons on the cylinder of a 3-manifold connect-summed with a 3-torus. En route…
Study abelian varieties' Weil-Petersson metric asymptotics.
problem Asymptotic behavior of Weil-Petersson metric on abelian varieties.
method Linking asymptotic with multi-scale collapsing limits of parametrized flat tori.
result Refined description of Weil-Petersson metric on abelian varieties.
We extend the methods of Davis-Januszkiewicz-Lafont to provide a new obstruction to smooth Riemannian metric with non-positive sectional curvature. We construct examples of locally CAT(0) 4-manifolds M, whose universal covers satisfy isolated flats condition and contain 2-dimensional flats with the property that $\sq…
New examples show Sasaki manifolds without extremal metrics.
problem Finding Sasaki manifolds without extremal metrics.
method Using Berglund-Hübsch transpose rule and relative K-stability.
result Examples of Sasaki manifolds without extremal metrics.
The paper solves PDEs from matrices with orthogonal columns, linking them to Hessian metrics and symmetric spaces.
problem Solving third order PDEs for strictly convex smooth functions.
method Geometric methods using Hessian metrics and symmetric spaces.
result Explicit solutions and a family of non-generic solutions with applications in Poisson geometry and Kahler structures.
Study shows Kähler-Einstein metric singularities linked to curvature.
problem Understanding singularities of Kähler-Einstein metrics.
method Relates singularities to holomorphic sectional curvature of conical geometry.
result Provides second-order estimates with explicit constants.
Formula for transgressions on polyhedral manifolds, linking face volumes and outer angles.
problem Computing topological invariants of polyhedral manifolds.
method Defining transgressions for Pfaffian of metric connections and applying to polyhedral manifolds.
result Derivation of an identity linking face volumes and outer angles of spherical and hyperbolic polyhedra.
We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such vector field be a member of the extremal set, the scalar curvature of a Sasaki extre…
New method fractures hyperbolic manifolds using cone singularities.
problem Deforming hyperbolic manifolds with cone singularities.
method Direct manipulation of a fundamental polyhedron to change cone angles.
result Upper unknotting tunnels of highly twisted links can be drilled out.
We present a new strategy for proving the Ambrose conjecture, a global version of the Cartan local lemma. A linking curve is defined as a curve in the tangent space whose composition with the exponential map is tree formed. This key idea is used to define sutured manifolds. We prove first that any sutured manifold sati…
For a holomorphic vector bundle E over a polarised Kähler manifold, we establish a direct link between the slope stability of E and the asymptotic behaviour of Donaldson's functional, by defining the Quot-scheme limit of Fubini-Study metrics. In particular, we provide an explicit estimate which proves that Donaldso…
Study on scalar curvature decay on non-compact manifolds linked at infinity.
problem Understanding scalar curvature decay on non-compact manifolds with topological linking at infinity.
method Analyzing polynomial decay, developing obstruction theory, using μ--bubble exhaustions, and index theory. result Topological linking at infinity forces polynomial decay of scalar curvature on manifolds of weakly bounded geometry.
A torsion-free G_2 structure admitting an infinitesimal isometry is shown to give rise to a 4-manifold equipped with a complex symplectic structure and a 1-parameter family of functions and 2-forms linked by second order equations. Reversing the process in various special cases leads to the construction of explicit met…
Study on 3-manifolds finds regular conformal metrics for rough metrics.
problem Characterize conformal metrics for rough Riemannian metrics on 3-manifolds.
method Analogous to the Yamabe problem, study conformal classes and regularity.
result Characterize when a more regular representative exists in the conformal class.
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other parts of Physics.
To a link L in the 3-sphere, we associate a spectral sequence whose E^2 page is the reduced Khovanov homology of L and which converges to a version of the monopole Floer homology of the branched double cover. The pages E^k for k > 1 depend only on the mutation equivalence class of L. We define a mod 2 grading on the sp…