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.
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…
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.
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.
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.
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.
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.
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…
Paper proves curvature conditions are preserved in metric spaces.
problem Preserving curvature conditions in metric spaces.
method Doubling and gluing constructions to preserve RCD(K,N) condition. result Proves RCD(K,N) condition is preserved. This paper aims to describe the behavior of diffeological differential forms under the operation of gluing of diffeological spaces along a smooth map. In the diffeological context, two ways of looking at diffeological forms are available, that of the vector space of all diffeological forms on a given space, and that of…
The study glues CAT(0) subsets of the plane under certain curvature conditions.
problem Understanding how to combine locally CAT(0) spaces. method Describes a gluing process for subsets of the Euclidean plane that maintain the CAT(0) property. result The gluing of two CAT(0) subsets, under specific curvature conditions, results in another CAT(0) space. 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.
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 Γ-invariant ASD connections on connected sums. 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…
New metrics with constant Q-curvature created by gluing.
problem Creating metrics with constant Q-curvature on spheres with punctures.
method Gluing truncated known metrics together.
result Unmarked moduli space of solutions is nontrivial for at least four punctures.
We give elementary constructions of manifold with corner structures and associative gluing maps on compactifications of spaces of infinite, half infinite, and finite Morse flow lines.
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.
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.
New method for constructing gluing parameterizations in geometric analysis.
problem Constructing gluing parameterizations for anti-self-dual connections.
method Using C1 maps of smooth Banach manifolds with corners. result Provides a method applicable to other nonlinear PDE problems.
Researchers create a method to join hyperboloidal data sets without violating the shear-free condition.
problem Creating consistent initial data sets for simulations of spacetime.
method Developed a new gluing procedure that maintains the shear-free condition using special Hölder spaces and elliptic operators.
result Successfully constructed hyperboloidal initial data sets that preserve the shear-free condition.
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 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.
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.
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 develop some consequences of the connection between Calabi-Yau structures and torsion-free G2 structures on compact and asymptotically cylindrical six- and seven-dimensional manifolds. Firstly, we improve the known proof that matching asymptotically cylindrical Calabi-Yau threefolds can be glued. Secondly, we giv…
Characterizes metrics on triangulated surfaces using glued Euclidean triangles.
problem Describing metrics on triangulated surfaces constructed from glued Euclidean triangles.
method Carefully constructing polyhedral metrics and proving their uniqueness.
result Polyhedral metrics are the only intrinsic metrics preserving Euclidean triangle lengths.
Develops gluing theory for contact instantons and pseudoholomorphic curves.
problem Constructing contact instanton Floer cohomology and Fukaya-type category.
method Gluing theory of contact instantons and pseudoholomorphic curves in symplectization context.
result Construction of Legendrian contact instanton homology and moduli spaces of holomorphic buildings.
Although our main interest here is developing an appropriate analog, for diffeological vector pseudo-bundles, of a Riemannian metric, a significant portion is dedicated to continued study of the gluing operation for pseudo-bundles introduced in arXiv:1509.03023. We give more details regarding the behavior of this opera…
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.
This paper is motivated by a relatively recent work by Joyce in special Lagrangian geometry, but the basic idea of the present paper goes back to an earlier pioneering work of Donaldson in Yang--Mills gauge theory; Donaldson discovered a global structure of a (compactified) moduli space of Yang--Mills instantons, and a…
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.
Extends Perelman's theorem to positive intermediate curvature conditions.
problem Positive intermediate curvature conditions and their implications.
method Generalization of Perelman's gluing theorem to positive intermediate curvature conditions.
result Observer moduli space can have non-trivial higher homotopy groups.
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…
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.
Proves Einstein metrics can be created by gluing perturbations.
problem Obstructs desingularization of Einstein orbifolds.
method Develops gluing-perturbation procedure for Einstein metrics.
result Extends Biquard's obstruction to more general cases.
Complete Calabi-Yau metrics made on special 3D spaces.
problem Creating complete Calabi-Yau metrics on complex 3D spaces.
method Used gluing construction and perturbation argument.
result Produced complete Calabi-Yau metrics with unbounded curvature.
Constructs many black hole spacetimes in de Sitter space.
problem Creating well-controlled many black hole spacetimes in de Sitter space.
method Gluing Schwarzschild-de Sitter or Kerr-de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions.
result Solves the Einstein equation directly for the metric, given scattering data at the future conformal boundary.
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 establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely …
New method to prove nonarithmeticity of hyperbolic gluings.
problem Proving nonarithmeticity of hyperbolic gluings.
method Determining adjoint trace fields of gluings.
result Many new examples of nonarithmetic gluings.
The techniques developed by Butscher in arXiv:math/0703469 for constructing constant mean curvature (CMC) hypersurfaces in the (n+1)-sphere by gluing together spherical building blocks are generalized to handle less symmetric initial configurations. The outcome is that the approximately CMC hypersurface obtained by glu…
We consider the diffeological pseudo-bundles of exterior algebras, and the Clifford action of the corresponding Clifford algebras, associated to a given finite-dimensional and locally trivial diffeological vector pseudo-bundle, as well as the behavior of the former three constructions (exterior algebra, Clifford action…
Smoothly attaches manifolds with controlled curvature.
problem Attaching manifolds with corners and controlling curvature.
method Desingularization theorem to smoothly attach manifolds with controlled scalar and mean curvature.
result Smoothly attaches manifolds with controlled scalar curvature and mean curvature of boundary.
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…
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 series invariants for plumbed 3-manifolds and their properties.
problem Understanding series invariants for plumbed 3-manifolds and their applications.
method Twisted root lattice, gluing and splitting properties, explicit description of lens spaces and Brieskorn spheres.
result Series verify gluing and splitting properties of 3-manifolds.
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.
Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature ≥κ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure spaces…