Spinors prove rigidity for polyhedral spacetime data.
problem Rigidity of polyhedral spacetime data sets.
method Extending rigidity analysis from spacetime positive mass theorem.
result Dihedral rigidity connects mass theorem, trapped surfaces.
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168,695 papers · 148 categories
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48 results for “rigid sets”
Finite rigid sets found in complex of curves for surfaces.
problem Finding finite rigid sets in curve complexes of surfaces.
method Exhaustion by finite rigid sets proved for surfaces of finite type and genus ≥3.
result Finite rigid sets exist in the non-separating curve complex of surfaces.
Finite rigid sets found in surface curve complexes.
problem Finding rigid sets in surface curve complexes.
method Incidence-preserving maps to find rigid subcomplexes.
result Finite rigid subcomplexes identified in surface curve complexes.
For an orientable surface of finite topological type with genus , we construct a finite set of curves whose union of iterated rigid expansions is the curve graph of . The set constructed, and the method of rigid expansion, are closely related to Aramayona and Leiniger's finite rigid set, and in fact a …
Finite rigid sets found in sphere complexes for some but not all cases.
problem Characterizing finite rigid sets in sphere complexes.
method Analyzing locally injective maps and automorphisms.
result Finite rigid sets exist for but not for .
Examines how irreducibility and rigidity affect digital images.
problem Understanding interactions between irreducibility and rigidity in digital images.
method Analyzes Cartesian products, wedges, and cold and freezing sets.
result Interactions between irreducibility and rigidity in digital images.
Paper proves rigidity of initial data sets with boundary and capillary MOTS.
problem Rigidity of initial data sets with boundary and capillary MOTS.
method Estimates area of MOTS, proves rigidity for 3D, extends to high dimensions using Yamabe constant.
result Rigidity results for initial data sets with boundary and capillary MOTS.
Rigidity results for initial data sets related to the positive mass theorem.
problem Rigidity of initial data sets in general relativity.
method Establishing conditions for weak outermost marginally outer trapped surfaces and rigidity results for Riemannian manifolds.
result Marginally outer trapped surfaces are weakly outermost under certain conditions.
Proves rigidity for specific initial data sets under the dominant energy condition.
problem Rigidity of initial data sets with boundary and convex polytopes.
method Solution of boundary value problems for Dirac operators and approximations by manifolds with smooth boundary.
result Proves rigidity for compact smooth spin manifolds and convex polytopes under the dominant energy condition.
The paper proves rigidity results for compact initial data sets.
problem Understanding the structure of compact initial data sets.
method Proving rigidity results under specific conditions.
result Global version of the main result in [15] is obtained.
Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
problem Rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
method Survey and observation on Cheeger-Yau inequality on RCD spaces.
result Observations on the Cheeger-Yau inequality and its applications.
The paper proves a spacetime version of dihedral rigidity for cubes in 3D spacetime.
problem Proving dihedral rigidity for cubic initial data sets in 3D spacetime.
method By studying the level sets of spacetime harmonic functions and extending previous work on dihedral rigidity for prisms in hyperbolic space.
result The paper proves dihedral rigidity for cubes in 3D spacetime, extending previous results.
A rigid set in a curve complex of a surface is a subcomplex such that every locally injective simplicial map from the set into the curve complex is induced by a homeomorphism of the surface. In this paper, we find finite rigid sets in the curve complexes of connected non-orientable surfaces of genus with holes …
Entropy rigidity proven for 3D and higher convex projective manifolds.
problem Entropy rigidity for strictly convex projective manifolds.
method Uses techniques from Besson, Courtois, and Gallot's entropy rigidity theorem.
result Uniform lower bounds on volume for finite volume strictly convex projective manifolds in dimensions ≥ 3.
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups).
Study inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.
problem Inequalities involving torsional rigidity and spherical deficit on Riemannian manifolds.
method Establish inequalities and derive an integral identity for a Dirichlet problem.
result Characterize metric balls and measure spherical deficit on Riemannian manifolds.
New method proves length spectrum rigidity in various geometric settings.
problem Length spectrum rigidity in geometric settings.
method Combination of dynamical systems and geometric group theory.
result Provides concise proofs and extends classical results.
Bi-Lipschitz rigidity theorem for dense subgroups of algebraic groups.
problem Characterizing dense subgroups of algebraic groups.
method Bi-Lipschitz rigidity theorem for Zariski dense discrete subgroups.
result No -smooth slim limit set for higher rank semisimple algebraic groups.
We construct uncountably many simply connected open 3-manifolds with genus one ends homeomorphic to the Cantor set. Each constructed manifold has the property that any self homeomorphism of the manifold (which necessarily extends to a homeomorphism of the ends) fixes the ends pointwise. These manifolds are complements …
Groups acting on product trees are boundary rigid.
problem Understanding boundary rigidity of groups acting on product trees.
method Analyzing geometric actions and visual boundaries of groups.
result Visual boundaries of CAT(0) spaces are homeomorphic to a join of two Cantor sets.
We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the "exotic" examples obtained by Katok and Lewis and the first author, by blowing up closed orbits in the well known actions on homogeneous spac…
Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data setsmath.DG
Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
problem Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
method Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets
result Prove area-charge inequalities for free boundary MOTS in initial data sets for the Einstein-Maxwell equations with vanishing magnetic fields
The paper explores conditions for topological rigidity in quotients of the Davis complex.
problem Understanding when quotients of the Davis complex are topologically rigid.
method Analyzing quotients of the Davis complex of right-angled Coxeter groups and conditions on defining graphs.
result Introduction of infinitely many infinite topologically rigid subclasses.
We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected compact Riemannian surface without conjugate points. For the more general class of non-trapping compact Riemannian surfaces with no conjugat…
We study Riemannian manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound. In our weighted setting, we prove several rigidity theorems for such manifolds with boundary. We conclude a rigidity theorem for the inscribed radii, a volume growth rigidity theorem for the metric neighborhoods of the boundar…
The paper discusses rigidity results for inequalities on weighted Riemannian manifolds.
problem Rigidity of inequalities on weighted Riemannian manifolds.
method Theorems of rigidity on curvature and measure for the Borell-Brascamp-Lieb inequality, generalizing a theorem by Balogh and Kristály.
result A generalization of the curvature rigidity theorem to the weighted setting.
New rigidity results for scalar curvature with stabilized conditions.
problem Establishing rigidity for scalar curvature with stabilized conditions.
method Construction of foliations and development of a monotone quantity using Ricci flow and heat equation.
result Generalized classical scalar curvature rigidity results to the \(T^{
times}\)-stabilized setting.
Let be a connected orientable surface of finite topological type. We prove that there is an exhaustion of the curve complex by a sequence of finite rigid sets.
This paper exhausts curve complexes on non-orientable surfaces.
problem Proving exhaustion of curve complexes on non-orientable surfaces.
method Proving exhaustion via rigid expansions and graph endomorphisms.
result Any graph endomorphism of curve complexes whose restriction to a finite rigid set is injective is induced by a homeomorphism.
Study proves rigidity of critical points in hydrophobic capillary systems.
problem Rigidity of critical points in hydrophobic capillary systems.
method Proves rigidity among sets of finite perimeter in the half space, extending to full hydrophobic regime.
result Rigidity of critical points proven in hydrophobic capillary systems.
The study finds sparse sets that uniquely determine metrics on negatively curved manifolds.
problem Determining metrics on negatively curved manifolds using spectral data.
method Analyzing conjugacy classes and marked length spectra.
result Sparse sets exist that uniquely determine metrics on negatively curved manifolds.
The paper proves a rigidity theorem for non-compact convex sets in hyperbolic 3-space.
problem Determining a closed convex set in hyperbolic 3-space by its boundary metric.
method Pogorelov's rigidity theorem, Hausdorff measure, and complex analysis techniques.
result The intrinsic path metric on the boundary determines a closed convex set up to isometry under certain conditions.
Paper proves new inequalities for Einstein-Maxwell data sets.
problem Establishing area-charge inequalities for Einstein-Maxwell initial data sets.
method Applying Gromov's μ-bubble technique in a new geometric context.
result Novel rigidity theorems for noncompact Einstein-Maxwell data sets.
Non-compact convex sets in hyperbolic 3-space are rigid under isometries.
problem Rigidity of non-compact convex sets in hyperbolic 3-space
method Proving rigidity using Pogorelov's theorem and properties of locally convex surfaces
result Any intrinsic isometry between the boundaries of two non-compact closed convex subsets extends to a global isometry of the ambient space
Surveying recent progress on hyperbolic 3-manifold rigidity.
problem Profinite rigidity of hyperbolic 3-manifolds.
method Review of profinite completion and rigidity of groups, evidence from other types of 3-manifolds, and existing ideas.
result Positive evidence for profinite rigidity in hyperbolic 3-manifolds.
Article strengthens initial data rigidity theorem to show unique spacetime extension.
problem Initial data rigidity in spacetime geometry.
method Showed initial data sets carry a lightlike parallel vector field, leading to unique spacetime extension.
result Local uniqueness of spacetimes extending initial data sets under dominant energy condition.
This study exhausts curve graphs of low-genus surfaces.
problem Exhausting curve graphs of low-genus surfaces.
method Constructing finite subgraphs and using rigid expansions.
result Graph morphisms and endomorphisms are automorphisms and induced by homeomorphisms.
Profinite rigidity proven for many hyperbolic manifolds.
problem Profinite rigidity of hyperbolic manifolds.
method Geometric topology and bubble-drilling construction.
result Profinite rigidity of many cusped hyperbolic manifolds.
Study proves rigidity of specific self-shrinkers under certain geometric conditions.
problem Proving rigidity of self-shrinkers under geometric constraints.
method Analyzing complete self-shrinkers with specific tangent planes.
result Sphere, plane, and cylinder are the only self-shrinkers under the given geometric assumption.
Researchers prove rigidity of convex polytopes in hyperbolic space using spinor techniques.
problem Proving rigidity of convex polytopes in hyperbolic space.
method Spinor techniques and recent smoothing constructions of Brendle-Wang.
result Scalar curvature rigidity for parabolic convex polytopes in hyperbolic space.
In \cite{BK02}, M. Bonk and B. Kleiner proved a rigidity theorem for expanding quasi-Möbius group actions on Ahlfors -regular metric spaces with topological dimension . This led naturally to a rigidity result for quasi-convex geometric actions on CAT-spaces that can be seen as a metric analog to the "entrop…
New rigidity results for complex and quaternionic moment-angle manifolds.
problem Equivariant topological rigidity of complex and quaternionic moment-angle manifolds.
method Reduction to equivariant rigidity of quasitoric (or quoric) quotients and principal bundles.
result Full equivariant rigidity for manifolds with four-dimensional quoric quotients and primary rigidity for higher dimensions.
Alternative approach to rigidity of high-dimensional isometric immersions.
problem Rigidity of high-dimensional isometric immersions between compact manifolds.
method Quantitative rigidity estimates, reducing to Euclidean setting and applying Friesecke-James-Müller rigidity estimate.
result Quantitative results showing close proximity to isometric immersions for small stretching and bending energy.
The paper proves energy theorems for specific initial data sets in 3D spacetime.
problem Establishing energy theorems for specific initial data sets in 3D spacetime.
method Analysis of level sets of spacetime harmonic functions.
result Rigidity results showing vanishing total energy imply isometric manifolds.
New findings extend rigidity results to broader classes of manifolds.
problem Extending rigidity results to non-warped product spaces.
method Establishing rigidity theorems for manifolds conformal to those with nonnegative curvature.
result New families of manifolds exhibit scalar-mean rigidity.
Study finds rigid properties of boundary-free hypersurfaces in specific data sets.
problem Rigidity of free boundary hypersurfaces in initial data sets with boundary.
method Extending local splitting theorems and applying results on free boundary MOTS.
result Rigidity results for compact free boundary hypersurfaces in initial data sets with boundary.
The flip graph and arc complex of a surface are shown to have finite rigidity.
problem Finite rigidity of flip graph and arc complex for surfaces.
method Embedding the flip graph in the arc complex and leveraging finite rigidity of the flip graph.
result Finite rigidity of the flip graph implies finite rigidity of the arc complex.
In this paper we study the rigidity of infinite volume 3-manifolds with sectional curvature and finitely generated fundamental group. In-particular, we generalize the Sullivan's quasi-conformal rigidity for finitely generated fundamental group with empty dissipative set to negative variable curvature …