Abstract: Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
problem Relationship between Fenchel-Nielsen coordinates and shear coordinates on Riemann surfaces.
method Explicitly showed the Poisson bracket on shear coordinates induces the Fenchel-Nielsen bracket on gluing parameters.
result Poisson bracket on shear coordinates relates to Fenchel-Nielsen bracket on gluing parameters.
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.
We study a finite rank bundle F over a neighborhood of J-Holomorphic map Moduli Spaces, prove the exponential decay of the derivative of the gluing maps for F with respect to the gluing parameter.
We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled "point-particle" limits an…
Paper proves gluing formula for analytic torsions using Witten deformation for non-Morse functions.
problem Analyzing analytic torsions for non-Morse functions.
method Witten deformation, Mayer-Vietoris sequences, Vishik's theory of moving boundary problems.
result Novel, purely analytic proof of the gluing formula for analytic torsions.
This paper constructs Seiberg-Witten monopoles from harmonic spinors on 3-manifolds.
problem Constructing Seiberg-Witten monopoles from Z2-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 Z2-harmonic spinor. This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual Yang-Mills gauge theory to an ``infinite energy'' situation. We show that we can glue an infinite number of instantons, and that the resulting instantons ha…
New Morse theory techniques glue nontransverse flowlines.
problem Gluing nontransverse gradient flowlines in Morse theory.
method Adapted OBG techniques from Hutchings and Taubes to Morse theory.
result Explicit criteria for gluing certain flowlines.
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.
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.
We construct new type II ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as t→−∞, to a tower of two spheres. Their curvature operator changes sign. We allow two time-dependent parameters in our ansatz. We use perturbation theory, via fixed point arguments,…
Proposes a new deep learning model for uncertainty quantification and propagation.
problem High-dimensional uncertainty quantification and propagation problems.
method Integrates U-net with Gaussian Gated Linear Network (GGLN) to create GLU-net.
result Less complex architecture with 44% fewer parameters than existing models.
New Spin(7)-instantons constructed on Joyce's manifold.
problem Constructing Spin(7)-instantons on Joyce's compact manifold. method Gluing non-flat connections on local model spaces to a flat connection on the Spin(7)-orbifold. result More than 20,000 new four-parameter families of Spin(7)-instantons. 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.
Study glues 2D hyperbolic manifolds, deriving mass formulas.
problem Mass invariance and positivity for 2D hyperbolic manifolds.
method Maskit gluing construction, minimization, monodromy construction.
result Derive mass/entropy formulae for glued manifolds.
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.
Study of skein modules in 3-manifolds, showing non-injectivity results.
problem Understanding skein modules in 3-manifolds and their behavior under gluing.
method Extended Kauffman bracket skein modules to 3-manifolds with marking, introduced new maps and studied their properties.
result Non-injectivity of certain maps in stated skein modules, especially when quantum parameter is a root of 1.
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.
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 …
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…
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.
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 Ck-gluing theorem for vacuum gravitational fields in Bondi gauge. result Generalized the C2-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.
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.
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.
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 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…
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild-de Sitter or Kerr-de Sitter black hole metrics into neighborhoods of points on the future conformal boun…
Researchers create new triply periodic minimal surfaces by gluing saddle towers.
problem Creating triply periodic minimal surfaces without symmetry constraints.
method Gluing Karcher-Scherk saddle towers with phase differences and balancing under vertical interaction.
result Expands known triply periodic minimal surfaces into new 5-parameter families.
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…
Thurston introduced a technique for finding and deforming three-dimensional hyperbolic structures by gluing together ideal tetrahedra. We generalize this technique to study families of geometric structures that transition from hyperbolic to anti de Sitter (AdS) geometry. Our approach involves solving Thurston's gluing …
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…
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.
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 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…
The paper extends knot contact homology to tangles and proves a gluing formula.
problem Defining and proving invariants for tangles in R3. 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.
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 (n+1)-dimensional static spacetimes with cosmological constant. result Generalization of gluing theorems to higher dimensions, extending previous work on light cones.