We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the classical construction of Gromov and Piatetski-Shapiro (and generalizations) as well as certain gluings of pieces of commensurable arithmetic …
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48 results for “gluing method”
Constructs a solution operator for hyperbolic gluing in higher dimensions.
problem Solving the linearized constant scalar curvature equation at hyperbolic space.
method Constructs a solution operator with good support propagation properties.
result Extends the Mao-Oh-Tao gluing method to the hyperbolic setting, gaining two derivatives.
Study gluing event horizons of Minkowski and Schwarzschild spacetimes.
problem Gluing event horizons of different spacetimes.
method Nonperturbative, gluing results from Aretakis-Czimek-Rodnianski and Christodoulou's short pulse method.
result Construct examples of vacuum gravitational collapse to very slowly rotating Kerr black holes.
The paper discusses conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
problem Conditions for gluing multiple Alexandrov spaces into an Alexandrov space.
method Proposes a Gluing Conjecture and proves it under certain conditions.
result The Gluing Conjecture is true under specific conditions, generalizing Petrunin's Gluing Theorem.
Paper solves Einstein vacuum equations gluing problem with applications.
problem Solving characteristic gluing problem for Einstein vacuum equations.
method Codimension-10 gluing construction, relating charges to ADM energy, and localized version.
result Asymptotically flat data can be glued to Kerr spacetime with 10 charges.
Adds charged black holes to de Sitter space.
problem Gluing charged black holes into de Sitter space.
method Extends Hintz's result to Einstein-Maxwell system with positive cosmological constant, using Reissner-Nordström or Kerr--Newman--de Sitter black holes.
result Determines conditions for gluing black holes into de Sitter space.
Properties of glued knotsmath.GT
Study on knots formed by gluing ellipses, defining gluing degree.
problem Properties of glued knots.
method Defined gluing degree to relate to knot properties.
result Classified all knots up to gluing degree 6.
Develops a method to compute Morse homology for clean but not necessarily transverse intersections.
problem Computing Morse homology for clean but not necessarily transversely intersecting manifolds.
method Constructs minimal semi-global Kuranishi structures for moduli spaces of Morse trajectories, generalizing obstruction bundle gluing.
result Obtains iterated gluing equals simultaneous gluing, maintaining computability.
We construct constant mean curvature surfaces in euclidean space by gluing n half Delaunay surfaces to a non-degenerate minimal n-noid, using the DPW method.
We construct periodic monopoles (with singularities), i.e. monopoles on possibly singular at a finite collection of points, by gluing methods.
New method glues Lorentzian spaces, preserving curvature bounds.
problem Creating new spaces from existing ones in Lorentzian geometry.
method Introducing an amalgamation process for Lorentzian pre-length spaces.
result Gluing preserves upper curvature bounds in spacetimes.
Study geometry of surfaces glued along a curve.
problem Geometry of surfaces glued along a curve.
method Moving frame along the curve, developable surfaces defined.
result Developed geometric properties of glued surfaces.
We use the gluing method to give a refined description of the collapsing Calabi-Yau metrics on Calabi-Yau 3-folds admitting a Lefschetz K3 fibration.
Contact gluing maps are shown to be equivalent in sutured Floer homology.
problem Equivalence of contact gluing maps in sutured Floer homology.
method Established a conjecture by Zarev, showing the contact gluing map is equivalent to the sutured Floer homology gluing map.
result Contact gluing maps are equivalent in sutured Floer homology.
Paper glues characteristic data to Kerr spacetime, proving spacelike gluing.
problem Solving characteristic gluing problem for Einstein vacuum equations.
method Detailed characteristic gluing of strongly asymptotically flat data to Kerr spacetime.
result Alternative proof of spacelike gluing construction for strongly asymptotically flat spacelike initial data.
New approach removes obstructions in gluing spacelike and null hypersurfaces in Einstein equations.
problem Gluing two solutions of the Einstein equations along a hypersurface.
method Active utilization of nonlinearity, low-frequency linear analysis, high-frequency nonlinear control.
result Removes 10-dimensional obstructions in null and spacelike gluing problems.
The purpose of this paper is to prove a gluing theorem for a given special Lagrangian submanifold of a Calabi-Yau 3-fold. The proof will be an adaption of the gluing techniques in J-holomorphic curve theory. It is a well known procedure in geometric analysis to construct new solutions to a given nonlinear partial diffe…
We describe a new approach to the problem of constructing gluing parameterizations for open neighborhoods of boundary points of moduli spaces of anti-self-dual connections over closed four-dimensional manifolds. Our approach employs general results from differential topology for maps of smooth Banach manifolds wi…
In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth st…
This paper constructs Seiberg-Witten monopoles from harmonic spinors on 3-manifolds.
problem Constructing Seiberg-Witten monopoles from -harmonic spinors on 3-manifolds.
method Gluing construction with alternating iteration to cancel infinite-dimensional obstruction bundle.
result A 1-parameter family of Seiberg-Witten monopoles converging to a -harmonic spinor.
The paper constructs gluing maps for harmonic maps between Riemannian manifolds.
problem Constructing harmonic maps between Riemannian manifolds.
method Gluing construction of extended harmonic maps.
result Construction of gluing maps for harmonic maps under specific conditions.
In this paper we announce a gluing theorem for conformal structures with anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that are more general than those considered by previous authors. By adapting a method proposed by Floer, sufficient conditions are given for the existence of ASD conformal str…
Researchers prove a nonlinear gluing theorem for gravitational fields near static backgrounds.
problem Proving a nonlinear gluing theorem for gravitational fields near static backgrounds.
method Proved a nonlinear characteristic -gluing theorem for vacuum gravitational fields in Bondi gauge.
result Generalized the -gluing theorem near light cones to a wider class of hypersurfaces.
Formulae connect heat kernels on glued manifolds.
problem Connecting heat kernels on joined manifolds.
method Proved gluing formulae for Laplacian heat kernels.
result Formulae linking heat kernels on joined manifolds.
Solves C^3 null gluing problem for Einstein vacuum equations.
problem Null gluing of up to third-order derivatives of the metric in Einstein vacuum equations.
method Linear and nonlinear analysis of characteristic data close to Minkowski data.
result Solvable up to a 20-dimensional space of obstructions, 10 of which are novel.
New method glues Scherk surfaces into minimal surfaces, limiting possible outcomes.
problem Limiting the outcomes of gluing Scherk surfaces into minimal surfaces.
method Constructing minimal surfaces by stacking and gluing doubly periodic Scherk surfaces.
result Except for special cases, gluing more Scherk surfaces results in known minimal surfaces.
We survey known (and unknown) results about the behavior of Heegaard genus of 3-manifolds constructed via various gluings. The constructions we consider are (1) gluing together two 3-manifolds with incompressible boundary, (2) gluing together the boundary components of surface times I, and (3) gluing a handlebody to th…
Simplified proof of gluing formula for analytic torsion forms.
problem Proving the gluing formula for analytic torsion forms.
method Extending prior work to the family case, presenting a new proof.
result Simplified proof of the gluing formula.
Study general hyperbolic gluings, proving quasi-arithmeticity of building blocks.
problem Proving quasi-arithmeticity of building blocks in hyperbolic gluings.
method Generalized gluings of hyperbolic orbifolds, proving quasi-arithmeticity.
result Building blocks of quasi-arithmetic gluings must also be quasi-arithmetic.
The paper classifies surfaces formed by quadrilateral gluings.
problem Classifying topological surfaces formed by quadrilateral gluings.
method Review of graphs embedded into surfaces, algorithms based on labeling schemes of fundamental polygons.
result Computing numbers of possible gluings for classification.
We present a gluing formula for Gromov-Witten invariants in the case of a triple product. This gluing formula is a simple case of a much more general gluing formula proved and stated using exploded manifolds. We present this simple case because it is relatively easy to explain without any knowledge of exploded manifold…
Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.
problem Deformation of Lipschitz homeomorphisms
method Lipschitz analogues of Siebenmann's and Perelman's homeomorphism theory
result Lipschitz stability theorem and gluing theorem
This paper studies the associativity of gluing of trajectories in Morse theory. We show that the associativity of gluing follows from of the existence of compatible manifold with face structures on the compactified moduli spaces. Using our previous work, we obtain the associativity of gluing in certain cases. In partic…
Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.
problem Behavior of warped-QAC Calabi-Yau metrics on affine quadrics.
method Gluing construction for collapsing warped-QAC Calabi-Yau manifolds.
result Verification of Yang Li's conjecture on warped QAC Calabi-Yau metrics.
Paper discusses gluing formula for zeta-determinants with Robin boundary condition.
problem Computing zeta-determinants with Robin boundary condition.
method Uses BFK type gluing formula and computes differences with Dirichlet boundary condition.
result Computes zeta-determinant on a cylinder with Robin boundary condition.
Survey on gluing constructions under lower curvature bounds.
problem Understanding lower curvature bounds in various geometric contexts.
method Analyzes gluing constructions in smooth and non-smooth settings.
result Provides conjectures and theorems on synthetic lower Ricci curvature bounds.
We study how a gluing construction, which produces compact manifolds with holonomy G_2 from matching pairs of asymptotically cylindrical G_2-manifolds, behaves under deformations. We show that the gluing construction defines a smooth map from a moduli space of gluing data to the moduli space of torsion-free G_2-structu…
In a previous article we studied PGL(n,C)-representations of a 3-manifold via a generalization of Thurston's gluing equations. Neumann has proved some symplectic properties of Thurston's gluing equations that play an important role in recent developments of exact and perturbative Chern-Simons theory. In this paper, we …
We study gluings of asymptotically cylindrical special Lagrangian submanifolds in asymptotically cylindrical Calabi--Yau manifolds. We prove both that there is a well-defined gluing map, and, after reviewing the deformation theory for special Lagrangians, prove that this gluing map defines a local diffeomorphism from m…
Local gluingmath.SG
Local gluing connects flow lines in finite time intervals.
problem Connecting flow lines in finite time intervals.
method Functional analytic approach to define local gluing map.
result Explicit construction of local gluing map in Euclidean case; intricate construction in non-Euclidean case.
In the previous article "Refined Analytic Torsion on Manifolds with Boundary" we have presented a construction of refined analytic torsion in the spirit of Braverman and Kappeler, which does apply to compact manifolds with and without boundary. We now derive a gluing formula for our construction, which can be viewed as…
In this article we use the adiabatic method to prove the gluing formula of real analytic torsion forms for a flat vector bundle on a smooth fibration under the assumption that the fiberwise twisted cohomology groups associated to the fibration of the cutting hypersurface are vanished. In this paper we assume that the m…
Tangle contact homologymath.SG
The paper extends knot contact homology to tangles and proves a gluing formula.
problem Defining and proving invariants for tangles in .
method Extending knot contact homology to tangles and proving a gluing formula.
result Tangle contact homology detects triviality of tangles.
Study gluing of Lorentzian length spaces and their causal ladder properties.
problem Compatibility of Lorentzian amalgamation with length space properties.
method Conditions for gluing Lorentzian length spaces and criteria for causal ladder preservation.
result Gluing of Lorentzian length spaces yields again a Lorentzian length space under certain conditions.
The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysisgr-qc
Solves Einstein vacuum equations gluing problem for close Minkowski data.
problem Solving the characteristic gluing problem for Einstein vacuum equations.
method Derived infinite-dimensional and 10-dimensional gauge-dependent and gauge-invariant charges; constructed null lapse function and conformal geometry.
result Obstructions to gluing problem are gauge-dependent charges, modulo gauge-invariant charges.
The paper extends gluing theorems for gravitational fields in higher dimensions.
problem Proving gluing theorems for linearised gravitational fields on characteristic hypersurfaces.
method Analyzing linearised vacuum gravitational fields in -dimensional static spacetimes with cosmological constant.
result Generalization of gluing theorems to higher dimensions, extending previous work on light cones.
Method constructs rigid associative submanifolds in twisted G2-manifolds.
problem Constructing rigid associative submanifolds in twisted G2-manifolds.
method Introducing a gluing theorem for asymptotically cylindrical associative submanifolds in ACyl G2-manifolds.
result Yields many new topological types of rigid associative submanifolds.
Gluing instantons on 4-manifolds with group action.
problem Gluing invariant ASD connections on 4-manifolds with group action.
method Equivariant gluing theory for instanton moduli spaces.
result Construction of -invariant ASD connections on connected sums.