Proves equivalence between Koebe circle domain conjecture and Weyl problem for hyperbolic surfaces.
problem Koebe circle domain conjecture and Weyl problem for convex surfaces in hyperbolic 3-space.
method Combining convex geometry and Schramm's transboundary extremal lengths.
result Equivalence between Koebe circle domain conjecture and Weyl problem for hyperbolic surfaces.
Minimal surfaces created from tiny circle packings changes.
problem Creating minimal surfaces from circle packings.
method Parametrizing deformations of circle packings and relating them to discrete minimal surfaces.
result Every minimal surface of Koebe type can be extended to a general type minimal surface.
In this paper we parametrize the Teichmüller spaces of constructible Koebe groups, that is Kleinian group that arise as covering of 2−orbifolds determined by certain normal subgroups of their fundamental groups. We also study the covering spaces of the Teichmüller spaces of those Koebe groups. Finally we prove an iso…
Paper extends circle pattern theory to obtuse angles.
problem Circle patterns with obtuse angles not previously covered.
method Using topological degree theory, extends Koebe-Andreev-Thurston Theorem.
result Generalized Andreev's Theorem for obtuse dihedral angles.
Paper centers Koebe polyhedra using Möbius transformations.
problem Centering Koebe polyhedra under Möbius transformations.
method Investigation of topological properties of integral curves in hyperbolic space.
result Most centers of Koebe polyhedra cannot be obtained as the center of a suitable measure defined on the sphere.
Article explores Thurston's circle packing theorem in 3-manifold geometry.
problem Understanding Thurston's circle packing theorem in 3-manifold geometry.
method Analyzes the Koebe-Andre'ev-Thurston Theorem and its relation to Thurston's circle packing theorem.
result Illustrates the significance of Thurston's circle packing theorem in 3-manifold geometry.
Historical notes on Thurston's 3-manifold geometry.
problem Exploring Thurston's notes on 3-manifold geometry.
method Historical commentary and references.
result Discussion of Lobachevsky, Andreev, and Milnor's works.
New discrete cmc surfaces defined from sphere packings and combinatorics.
problem Creating constant mean curvature surfaces from discrete data.
method Discrete cmc surfaces defined via sphere packings and combinatorial patterns.
result Construction of discrete cmc surfaces from orthogonal ring patterns.
Survey on discrete minimal surfaces and their properties.
problem Discretizing minimal surfaces in Euclidean space.
method Polyhedral surfaces with parallel face offsets and circle patterns.
result All simply connected discrete minimal surfaces can be constructed from circle patterns.
We prove existence and uniqueness results for patterns of circles with prescribed intersection angles in constant curvature surfaces. Our method is based on two new functionals--one for the Euclidean and one for the hyperbolic case. We show how Colin de Verdi`ere's, Br"agger's and Rivin's functionals can be derived fro…
New method connects compression bodies through cone manifolds.
problem Understanding how compression bodies can be transformed.
method Using cone manifold holonomy groups and standard CAT(0) space techniques. result Realized all edges in compression body graph through paths.
We approach the problem of uniformization of general Riemann surfaces through consideration of the curvature equation, and in particular the problem of constructing Poincaré metrics (i.e., complete metrics of constant negative curvature) by solving the equation Δu−e2u=K0(z) on general open surfaces. A few oth…
Unique circle patterns on spheres found for spherical conical metrics.
problem Non-uniqueness in circle packing for spherical metrics.
method Prescribed geodesic total curvature instead of cone angles.
result Unique existence of circle patterns for spherical conical metrics.
Paper calculates ball number of links using Lorentz geometry and circle packing.
problem Calculating the minimum number of balls needed to represent a link.
method Lorentz geometry and circle packing theorem applied to ball packings.
result Shows ball(L)≤5cr(L) for any link L. Let $(M, \dr M)$ be a 3-manifold with incompressible boundary that admits a convex co-compact hyperbolic metric. We consider the hyperbolic metrics on M such that $\dr M$ looks locally like a hyperideal polyhedron, and we characterize the possible dihedral angles. We find as special cases the results of Bao and Bonah…
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.
Let (M,∂M) be a compact 3-manifold with boundary which admits a complete, convex co-compact hyperbolic metric. For each hyperbolic metric g on M such that $\dr M$ is smooth and strictly convex, the induced metric on $\dr M$ has curvature K>−1, and each such metric on $\dr M$ is obtained for a unique ch…
The Weyl problem is extended to hyperbolic and anti-de Sitter spaces, connecting geometry, analysis, and group theory.
problem The classical Weyl problem for surfaces in hyperbolic and anti-de Sitter spaces.
method Generalizations of the Weyl problem to unbounded convex subsets and convex surfaces, focusing on thin and thick asymptotic boundaries.
result Connections to Kleinian groups, complex analysis, circle packings, and grafting on the hyperbolic disk.
Typilus predicts types for Python programs using neural networks.
problem Type inference in dynamically typed languages is challenging.
method Graph neural network model that predicts types by probabilistically reasoning over program structure, names, and patterns.
result Typilus can predict types for 70% of all annotatable symbols and type checks 95% of the predicted types.
LambdaNet infers TypeScript types using graph neural networks.
problem Automatic inference of TypeScript type annotations.
method Graph Neural Network for type dependency graph analysis.
result LambdaNet outperforms existing methods by 14%.
Study shows partially-typed NER datasets can match fully-typed ones in model performance.
problem Leveraging multiple partially-typed NER datasets for training models without fully-typed annotations.
method Systematic analysis and controlled experiments comparing partially-typed and fully-typed datasets.
result Models trained with partially-typed annotations can achieve similar performance to those trained with fully-typed annotations.
The generic fiber of a Lagrangian fibration on an irreducible holomorphic symplectic manifold is an abelian variety. Associate a polarization type to such Lagrangian fibrations coming from polarizations on a generic fiber. We prove that this polarization type is constant in families of Lagrangian fibrations. Further, w…
Paper introduces a new adversarial attack type that cheats classifiers with significant changes.
problem Cheating well-trained classifiers with small permutations.
method Supervised variation autoencoder and gradient-based updates to latent variables.
result The proposed attack significantly cheats classifiers with significant changes, reducing Type I error.
We analyze Darboux transformations in very general settings for multidimensional linear partial differential operators. We consider all known types of Darboux transformations, and present a new type. We obtain a full classification of all operators that admit Wronskian type Darboux transformations of first order and a …
Constructs odd Khovanov homotopy types for links, linking them to even types.
problem Understanding and constructing odd Khovanov homotopy types for links.
method Constructs stable homotopy types X^j_o(L) for links L, with cohomology matching odd Khovanov homology.
result Odd Khovanov homotopy types carry a Z/2 action whose fixed points are related to even Khovanov homotopy types.
Study shows infinite real homotopy types for complex nilmanifolds.
problem Understanding real homotopy types of complex nilmanifolds.
method Analyzing 2n-dimensional nilmanifolds with generalized complex structures. result Infinitely many real homotopy types exist for 2n-dimensional nilmanifolds. ptype infers data types robustly in real-world data.
problem Type inference fails with missing data and anomalies.
method Probabilistic robust type inference method.
result Outperforms existing methods.
Category theory generalizes finite type invariants using diagrams systems.
problem Generalizing finite type invariants using category theory.
method Relating generating sets for generalized finite type theories with diagrams systems.
result Demonstrates the correspondence between finite type theories and diagrams systems.
New spherical curve deformations solve a conjecture.
problem Solving the Östlund Conjecture for spherical curves.
method Introducing a new type of deformation (β) and proving equivalence under specific deformations.
result Equivalence of spherical curves under specific deformations.
Finite-type surfaces have a topological Hopf property.
problem Characterizing surfaces with a topological Hopf property.
method Using topological analogs of the Hopf property.
result Infinite-type surfaces do not have the Hopf property.
As entity type systems become richer and more fine-grained, we expect the number of types assigned to a given entity to increase. However, most fine-grained typing work has focused on datasets that exhibit a low degree of type multiplicity. In this paper, we consider the high-multiplicity regime inherent in data source…
Study shows transfer of adversarial robustness between different perturbation types is limited.
problem Understanding adversarial robustness across various perturbation types.
method Evaluated 32 attacks of 5 different types on models trained on a subset of ImageNet.
result Adversarial robustness transfer between perturbation types is limited and depends on the specific type of perturbation.
Kähler-Ricci flow singularity type is independent of initial metric.
problem Independence of singularity type for Kähler-Ricci flows.
method Analyzing solutions to the Kähler-Ricci flow on numerically effective manifolds.
result The singularity type of solutions is independent of the initial metric.
The paper defines a new equivalence relation for knot projections and finds an infinite number of distinct classes.
problem Classifying knot projections based on weak homotopy equivalence.
method Defining weak (1, 2, 3) homotopy and using it to find an invariant.
result There are an infinite number of weak (1, 2, 3) homotopy equivalence classes of knot projections.
We describe a bordered version of totally twisted Khovanov homology. We first twist Roberts's type D structure by adding a "vertical" type D structure which generalizes the vertical map in twisted tangle homology. One of the distinct advantages of our type D structure is that it is homotopy equivalent to a type $…
In the theory of finite type submanifolds, null 2-type submanifolds are the most simple ones, besides 1-type submanifolds (cf. e.g., [3, 12]). In particular, the classification problems of null 2-type hypersurfaces are quite interesting and of fundamentally important. In this paper, we prove that every δ(3)-ideal nul…
Extends techniques to show existence of all cusp types in convex projective manifolds.
problem Existence of all cusp types in convex projective manifolds.
method Extension of techniques by Ballas-Marquis.
result Existence of all cusp types in all dimensions except diagonalizable.
Study BF invariants using simple type concepts.
problem Understanding Bauer--Furuta invariants for 4-manifolds.
method Extend simple type concept to BF blowup and BF homogeneous types, prove gluing formulae and adjunction inequality.
result Determine Bauer--Furuta invariant of a specific 4-manifold and give constraints on gluing decompositions.
It is known that all left-invariant pseudo-Riemannian metrics on H3 are algebraic Ricci solitons. We consider generalizations of Riemannian H-type, namely pseudoH-type and pH-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transver…
Classifies special Lie algebras with semisimple types.
problem Classifying Lie algebras of semisimple type.
method Introduced conformal pseudo-subriemannian fundamental graded Lie algebras and provided their classification.
result Classification of conformal pseudo-subriemannian fundamental graded Lie algebras of semisimple type and their prolongations.
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
problem Understanding relationships between triangulations of infinite type surfaces via flips.
method Associate triangulations to flip graphs and study sequences of simultaneous flips.
result Flip graphs for infinite type surfaces have uncountably many connected components.
Crowdsourced labeling recovers task types with minimal queries.
problem Labeling tasks accurately with minimal queries.
method Worker clustering, skill estimation, weighted majority voting.
result Achieves any targeted recovery accuracy with minimum queries.
New extremal Poincaré type metrics found via blow-up theorem.
problem Finding new extremal Poincaré type metrics.
method Proved Arezzo-Pacard-Singer blow-up theorem for Poincaré type metrics and applied to new examples.
result Found new examples of extremal Poincaré type metrics with an additional obstruction.
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in this sense. We also generalize the approach to Milnor's higher order homotopy invariants and show that they are also, in a sense, of finite t…
Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.
problem Creating metrics with negative scalar curvature.
method Constructed two types of Eguchi-Hanson metrics.
result Found metrics with negative scalar curvature.
In this paper, we obtain a Cartan type identity for curvature-adapted isoparametric hypersurfaces in symmetric spaces of compact type or non-compact type. This identity is a generalization of Cartan-D'Atri's identity for curvature-adapted(=amenable) isoparametric hypersurfaces in rank one symmetric spaces. Furthermore,…
Extends A-type coefficient polynomials to B-type setting, introducing new invariants.
problem Tackles the B-type skein relation and introduces new coefficient polynomials.
method Introduces coefficient polynomials associated with the B-type skein relation and proves their invariance under Reidemeister moves.
result Shows that the generating series of these coefficient polynomials recovers the Kauffman polynomial.