Study 2-loop part of Johnson cokernel using trace map.
problem Identify components of Johnson cokernel in degree 6.
method Use 2-loop trace map to capture Johnson cokernels.
result Capture all components of Johnson cokernels in degree 6.
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48 results for “stable Sp-decomposition”
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
Stable Torsion Lengthmath.GR
Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.
problem Understanding the stable torsion length in groups, especially in crystallographic and free products of groups.
method Developed linear programming and exact algorithms to compute stable torsion length in free products of groups and finite groups.
result Showed that stable torsion length vanishes in crystallographic groups and provided exact computations for nontrivial examples.
Study on stable translation lengths of surface homeomorphisms and their approximations.
problem Understanding stable translation lengths of homeomorphisms and their finite approximations.
method Comparing stable translation lengths of homeomorphisms and their finite approximations on curve graphs.
result Stable translation length of homeomorphisms with dense periodic points equals the supremum of their approximations.
The paper extends stable minimal hypersurface results to δ-stable hypersurfaces in R^(n+1).
problem Extending stable minimal hypersurface results to δ-stable hypersurfaces.
method Regularity and compactness theorems for immersed δ-stable minimal hypersurfaces in R^(n+1).
result Optimal range of δ for δ-stable hypersurfaces.
Study on stable Hamiltonian topology finds non-density of certain structures.
problem Non-density of stable hypersurfaces and Hamiltonian structures.
method Proving non-density results for stable hypersurfaces and Hamiltonian structures in various dimensions.
result Non-density of stable hypersurfaces and Hamiltonian structures in specific isotopy and homotopy classes.
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their -var…
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
Stable minimal hypersurfaces in math.DG
Flat stable minimal hypersurfaces in 5D are always flat.
problem Characterizing stable minimal hypersurfaces in higher dimensions.
method Analyzing properties of stable minimal hypersurfaces in \(\mathbf{R}^5\).
result Complete, two-sided stable minimal hypersurfaces in \(\mathbf{R}^5\) are flat.
Characterizes hyperbolic links with stable maps to the plane.
problem Understanding hyperbolic links through stable maps.
method Characterization of hyperbolic links via stable maps to the plane.
result Complete characterization of hyperbolic links with specific stable maps.
Stable nets on convex hypersurfaces maintain their shape under small perturbations.
problem Maintaining the shape of nets on convex surfaces under slight changes.
method Constructing stable geodesic nets on convex hypersurfaces.
result Stable geodesic nets on convex hypersurfaces do not change shape under small perturbations.
Classifies normal stable Horikawa surfaces with smoothable singularities.
problem Characterizing surfaces with specific singularities and smoothability criteria.
method Classification and smoothability criterion based on log canonical singularities.
result Provides a criterion for global -Gorenstein smoothability of Horikawa surfaces.
The paper explores density of stable mappings and their properties.
problem Density of stable mappings in different dimensions.
method Infinitesimal and algebraic methods to prove density of proper stable and topologically stable mappings.
result Density of topologically stable mappings holds for any pair (n,p), and for proper stable mappings if (n,p) is in nice dimensions.
Paper calculates stable cohomology of universal degree d hypersurfaces.
problem Computing stable cohomology of universal degree d hypersurfaces.
method Uses stable cohomology and geometric description of stable classes.
result Geometric description of stable classes of universal degree d hypersurfaces.
New proof for stable reduction theorem using Kähler-Einstein metrics.
problem Proving the stable reduction theorem for curves over punctured curves.
method Using Kähler-Einstein metrics on fibers to obtain limiting stable curves.
result A new analytic proof of the stable reduction theorem for curves over punctured curves.
Defines super stable maps and proves quotient superorbifolds for genus zero.
problem Defines stable supercurves and super stable maps of genus zero.
method Uses labeled trees and slice theorem for super Lie groups.
result Proves moduli space of stable supercurves and super stable maps are quotient superorbifolds.
Paper proves every stable 4-sphere has a unique diffeomorphism class.
problem Identifying stable 4-spheres and their diffeomorphisms.
method Using Wall's result and properties of surface-knot spaces.
result Every stable 4-sphere has a unique orientation-preserving diffeomorphism class.
Weakly stable constant mean curvature (CMC) hypersurfaces are stable critical points of the area functional with respect to volume preserving deformations. We establish a pointwise curvature estimate (in the non-singular dimensions) and a sheeting theorem (in all dimensions) for weakly stable CMC hypersurfaces, giving …
Sharp upper bound found for stable minimal surfaces.
problem Bounding the diameter of stable minimal surfaces.
method Analyzing three-dimensional Riemannian manifolds with specific curvature conditions.
result Sharp upper bound for the diameter of stable minimal surfaces.
The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.
problem Exploring stable surfaces in static Einstein-Maxwell space-time.
method Using mean-stable surfaces theory to prove properties of lapse functions and mass bounds.
result Proves ADM mass is bounded by Hawking quasi-local mass.
The paper examines the behavior of Weierstrass measures on stable curves as they approach a nodal stable curve.
problem Understanding the behavior of Weierstrass measures on stable curves as they approach a nodal stable curve.
method Analyzing the limiting behavior of Weierstrass measures on a smooth curve of genus as it approaches a nodal stable curve in the Deligne-Mumford compactification.
result The Weierstrass measures on a stable rational curve at the boundary of are completely determined.
New structures allow for self-crossing singularities, leading to new families of stable generalized complex manifolds.
problem Stable generalized complex structures in higher dimensions with self-crossing singularities.
method Extending stable generalized complex structures to include anticanonical sections with normal self-crossings.
result Construction of large families of stable generalized complex manifolds in four dimensions.
The study restricts stable minimal immersions in product spaces to specific configurations.
problem Prohibiting stable minimal immersions in certain product spaces.
method Analyzing stable minimal immersions in products of complex, quaternionic, and octonionic projective spaces.
result The only stable compact minimal immersions in the product of a quaternionic projective space with any other Riemannian manifold are the products of quaternionic projective subspaces with compact stable minimal immersions of the second manifold.
We introduce the stable presentation length of a finitely presented group. The stable presentation length of the fundamental group of a 3-manifold can be considered as an analogue of the simplicial volume. We show that the stable presentation length have some additive properties like the simplicial volume, and the simp…
Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X,g), its real homology H_*(X,R) is naturally endowed with the stable norm. Briefly, if h\in H_k(X,R) then the stable norm of h is the infimum of the Riemannian k-volumes of re…
Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.
problem Classifying non-linear proper Fredholm maps between Hilbert spaces.
method Using stable homotopy groups of spheres to classify maps up to proper homotopy.
result Determines the non-trivial kernel of the map from stable homotopy groups to non-linear proper Fredholm maps.
For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then th…
We study the structure of the stable norm of Finsler metrics on the 2-torus with a focus to points of irrational slope. By our results, the stable norm detects KAM-tori and hyperbolicity in the geodesic flow. Moreover, we study the stable norm in some natural examples.
Stable minimal hypersurfaces in math.DG
Flat stable minimal hypersurfaces found in 6D space.
problem Existence of stable minimal hypersurfaces in .
method Adapted Chodosh-Li-Minter-Stryker strategy with volume estimates.
result Complete, two-sided stable minimal hypersurfaces in are flat.
In this paper, we study distribution of the zeros of the Alexander polynomials of knots and links in S^3. We call a knot or link "real stable" (resp. "circular stable") if all the zeros of its Alexander polynomial are real (resp. unit complex). We give a general construction of real stable and circular stable knots and…
Stable generalized complex structures on certain surfaces are constant.
problem Existence of stable generalized complex structures on ruled surfaces.
method Analysis of sphere bundles over surfaces of genus ≥2.
result Stable generalized complex structures on these surfaces are of constant type.
Lower bound on stable 4-genus of knots using Casson-Gordon signatures.
problem Finding a lower bound on the stable 4-genus of knots.
method Using Casson-Gordon τ-signatures to compute the lower bound.
result A twist knot is torsion in the knot concordance group if and only if it has vanishing stable 4-genus.
Study calculates stable norm of slit tori using Farey sequence.
problem Computing the stable norm of slit tori.
method Explicit computations using the Farey sequence and gluing slit tori.
result Estimates the asymptotic counting of simple homology classes.
New findings on stable minimal hypersurfaces in curved 4-manifolds.
problem Nonexistence of complete stable minimal hypersurfaces in positively curved 4-manifolds.
method Combination of non-negative sectional curvature and strict positivity of scalar curvature.
result Rigidity of complete stable minimal hypersurfaces in 4-manifolds with positive curvature.
Stable random variables are motivated by the central limit theorem for densities with (potentially) unbounded variance and can be thought of as natural generalizations of the Gaussian distribution to skewed and heavy-tailed phenomenon. In this paper, we introduce stable graphical (SG) models, a class of multivariate st…
Proof that stable minimal surfaces in 3D are flat.
problem Classification of stable minimal surfaces in .
method Index theory for Dirac operators on twisted spinor bundles.
result Every complete two-sided stable minimal surface in is flat.
We study the stable norm on the first homology of a closed, non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater tha…
Researchers prove a method to upgrade Morse-Bott homology to stable homotopy invariants.
problem Proving a method to upgrade Morse-Bott homology to stable homotopy invariants rigorously.
method Rigorous construction of stable normal framings and proof of stable homotopy type recovery.
result The stable homotopy type recovers Σ∞+M and Thom spectra for all reduced KO-theory classes.
Estimates for stable minimal hypersurfaces in Euclidean space.
problem Deriving estimates for stable minimal hypersurfaces.
method Derivation of estimates related to Bernstein theorems.
result Indicates limitations of existing methods for .
Stable solutions to Yang-Mills-Higgs equations on spheres and tori identified.
problem Stable solutions to abelian Yang-Mills-Higgs equations on and .
method Reduction to vortex equations and application of Bourguignon-Lawson's method for stable Yang-Mills connections.
result Stable solutions to abelian Yang-Mills-Higgs equations on and are identified as satisfying vortex equations.
We study the structure of the stable coefficients of the Jones polynomial of an alternating link. We start by identifying the first four stable coefficients with polynomial invariants of a (reduced) Tait graph of the link projection. This leads us to introduce a free polynomial algebra of invariants of graphs whose ele…
We investigate Chow stability of projective bundles P(E) where E is a strictly Gieseker stable bundle over a base manifold that has constant scalar curvature. We show that, for suitable polarisations L, the pair (P(E),L) is Chow stable and give examples for which it is not asymptotically Chow stable.
New method proves -principles for stable forms on manifolds.
problem Proving -principles for stable forms on manifolds.
method Convex integration applied to stable forms.
result Proved -principles for 4 classes of stable forms.
The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on H_{n-1}(M,R) is a homogenized version of the Riemannian (n-1)-volume. We study…
Non-compact manifolds prevent -stable mappings from being dense.
problem Density of -stable mappings on non-compact manifolds.
method Using topologically critical points to show non-density.
result The set of -stable mappings is never dense on non-compact manifolds.
Study improves curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.
problem Curvature estimate for stable marginally outer trapped hypersurfaces with a free boundary.
method Iteration argument based on uniform area bound.
result Improved curvature estimate for stable marginally outer trapped hypersurfaces.
Turaev's shadow can be seen locally as the Stein factorization of a stable map. In this paper, we define the notion of stable map complexity for a compact orientable 3-manifold bounded by (possibly empty) tori counting, with some weights, the minimal number of singular fibers of codimension 2 of stable maps into the re…
The study shows properties of stable anisotropic minimal hypersurfaces in 4D space.
problem Characterizing stable anisotropic minimal hypersurfaces in .
method Analyzing the intrinsic cubic volume growth and interior volume upper bounds for stable anisotropic minimal hypersurfaces.
result Explicit estimates of constants for stable anisotropic minimal hypersurfaces in .