Crosscap Stabilitymath.DG
Crosscaps remain stable under smooth deformations.
problem Stability of crosscaps under smooth transformations.
method Alternative proof using diffeomorphisms.
result Crosscaps are diffeomorphically stable.
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48 results for “Stability under deformation”
Study shows stability of locally conformally balanced condition under modifications but not under small deformations.
problem Stability of locally conformally balanced condition under small deformations and modifications.
method Proved stability under proper modifications and instability under small deformations using examples and Hilbert-Chow map.
result Stability of locally conformally balanced condition under proper modifications and instability under small deformations.
Stability of SKT metrics under deformations on complex manifolds.
problem Stability of strong Kähler with torsion metrics under small deformations.
method Finding necessary conditions for stability of SKT metrics along a family of complex manifolds.
result Necessary conditions for the stability of SKT metrics on a smooth curve of Hermitian metrics.
Symplectic forms can be preserved under small deformations on Calabi-Yau manifolds.
problem Preserving symplectic forms under deformations on Calabi-Yau manifolds.
method Dynamical stability of symplectic curvature flow.
result Any small symplectic deformation of a Kähler form remains Kähler on a compact Calabi-Yau manifold.
Study on stability of Sasaki structures under deformations.
problem Stability of Sasaki structures under transverse holomorphic deformations.
method Analysis of transverse Kähler holonomy groups and stability properties.
result Stability of ${\oldmathcal S}$ under certain conditions on Sasaki manifolds.
We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relati…
Local stability of p-Kähler structures studied.
problem Stability of p-Kähler structures under deformations.
method Natural extension map and power series method.
result Local stability theorem for p-Kähler structures.
In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which a…
Study shows curvature stability under smooth metric convergence.
problem Stability of nonnegative isotropic curvature under metric deformations.
method Introduced method by R. Bamler to study scalar curvature behavior.
result Proved that if metrics converge in C0 norm, resulting metric has isotropic curvature bounded from below.
Study on deformations of Lie groupoid morphisms and their properties.
problem Understanding the deformation theory of Lie groupoid morphisms.
method Established deformation theory, cohomology, and properties of morphisms.
result Invariance and stability properties of morphisms, Morita invariance of cohomology, and simultaneous deformations.
In this article we develop a new approach to the problem of the stability of locally conformally Kähler structures (l.c.k structures) under small deformations of complex structures and deformations of flat line bundles. We show that under the certain cohomological condition the stability of l.c.k structures does hold. …
Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.
problem Ensuring the Kähler property of Calabi-Yau 3-folds under symplectic deformations.
method Established dynamical stability of Type IIA flow near stationary points.
result Stability of Type IIA flow ensures the stability of Kähler properties under symplectic deformations.
Surveying stability and deformation of Einstein metrics.
problem Stability and deformation of Einstein metrics.
method Study of the spectrum and eigentensors of the Lichnerowicz Laplacian.
result Recent results on stability and deformation theory of Einstein metrics.
Dynamical Stability of Minimal Lagrangians in Kähler-Einstein Manifolds of Non-Positive Curvaturemath.DG
Minimal Lagrangians in certain curved spaces are stable under specific flows.
problem Stability of minimal Lagrangians in Kähler-Einstein manifolds of non-positive curvature.
method Proved stability under Lagrangian mean curvature flow.
result Equivalence between linear and dynamical stability for -close Lagrangians.
Paper proves stability of pseudo-Einstein contact form existence.
problem Stability of pseudo-Einstein contact form existence under deformations.
method Deformations of real hypersurfaces in complex manifolds.
result Existence of pseudo-Einstein contact form is preserved under deformations.
Study shows existence of Strominger system solutions is not stable under complex structure deformations.
problem Stability of Strominger system solutions under complex structure deformations.
method Analyzes stability of solutions to the Strominger system in dimensions six, considering both positive and negative slope parameters.
result Existence of solutions to the Strominger system is neither open nor closed under holomorphic deformations of the complex structure.
The paper proves stability for contact groupoids and deformations.
problem Stability of contact groupoids and deformations.
method Proof of Gray stability for compact contact groupoids.
result Stability results for deformations of induced Jacobi bundles.
Harmonic functions stable under small changes.
problem Stability of multivalued harmonic functions under deformations.
method Application of Nash-Moser implicit function theorem.
result Stability of harmonic sections under small deformations.
Pooling is not essential for image classification stability.
problem The necessity of pooling for image classification stability.
method Rigorous empirical testing of CNNs without pooling.
result Pooling is neither necessary nor sufficient for optimal deformation stability in CNNs.
Introduces relative stability conditions on triangulated categories.
problem Stability conditions in triangulated categories.
method Definition and deformation of relative stability conditions.
result Deformation of relative stability conditions via gluing stability conditions.
New deformation stability for cartoon functions proved.
problem Deformation stability of deep CNNs for cartoon functions.
method Established bounds for cartoon functions.
result Deformation stability for cartoon functions proved.
Study helicoidal surfaces from frontals, revealing geometric rigidity and stability of singularities.
problem Investigate helicoidal surfaces of frontals in Euclidean space.
method Using Legendre curves and framed surfaces, derive curvature expressions and analyze deformations.
result Singularities of curves persist under deformations, revealing geometric rigidity and stability.
Study higher rank deformed Hermitian-Yang-Mills equations for stable vector bundles.
problem Stability conditions for higher rank vector bundles over complex manifolds.
method Establish equivalence between dHYM equations and -stability.
result Equivalence between dHYM solutions and -stability for vortex type bundles.
Study on stability of α-harmonic maps and their applications.
problem Investigating the stability of α-harmonic maps and their physical applications.
method Non-existence theorem, conformal deformation, Ricci curvature analysis, α-stable manifolds.
result Investigation of the instability of non-constant α-harmonic maps and their physical applications.
We introduce -critical connections for holomorphic vector bundles and prove their existence under stability conditions.
problem Existence of -critical connections for holomorphic vector bundles.
method Associated geometric PDEs to Bridgeland stability conditions and used infinite dimensional moment maps.
result In the large volume limit, a sufficiently smooth holomorphic vector bundle admits a -critical connection if and only if it is asymptotically -stable.
Study on deformations of -forms and spectral sequence degenerations.
problem Understanding deformations of -forms under complex structure changes.
method Analyzing Frölicher spectral sequence conditions for -form deformations.
result Unobstructed deformations of -forms under specific spectral sequence conditions.
Study higher rank deformed Hermitian-Yang-Mills equations for stable vector bundles.
problem Stability conditions for higher rank vector bundles over complex manifolds.
method Establish equivalence between dHYM equations and -stability.
result Equivalence between dHYM solutions and -stability for vortex type bundles.
Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.
problem Solvability of the deformed Hermitian-Yang-Mills equation and its relation to geometric stability.
method Utilizing geometric invariant theory (GIT) and Bridgeland stability theory to analyze the equation.
result On the blow-up of \(\mathbb{P}^2\), line bundles admitting a solution of the deformed Hermitian-Yang-Mills equation are Bridgeland stable, but not conversely.
Study shows how to reduce data needed for learning under geometric constraints.
problem Learning high-dimensional data with geometric priors.
method Spherical harmonic decompositions and kernel methods for invariance and geometric stability.
result Improvements in sample complexity by leveraging group invariance, with asymptotic behavior depending on spectral properties.
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
Simplified proof of stability for Ricci flow near ALE metrics.
problem Stability of Ricci flow near ALE metrics with integrable deformations.
method Equivalence between integrability and almost-orthogonality property of Ricci-DeTurck tensor, analysis in weighted Holder spaces.
result Dynamical stability of Ricci flow near linearly stable Ricci-flat ALE metrics.
We show that every finite volume hyperbolic manifold of dimension greater or equal to 3 is stable under rescaled Ricci flow, i.e. that every small perturbation of the hyperbolic metric flows back to the hyperbolic metric again. Note that we do not need to make any decay assumptions on this perturbation. It will turn ou…
Stable algebraic filters improve neural network performance.
problem Improving neural network stability to deformations.
method Analyzed stability of algebraic filters and neural networks under deformations of the homomorphism.
result Stable algebraic filters have frequency responses whose derivative is inversely proportional to frequency.
Study on scalar curvature deformations in pseudohermitian manifolds.
problem Deformation of scalar curvature in pseudohermitian manifolds.
method Analogy with Riemannian manifolds, introduction of -singular spaces, stability conditions, partial infinitesimal rigidity.
result Partial infinitesimal rigidity result for scalar curvature of compact pseudohermitian manifolds.
The study examines stability of specific geometric flows.
problem Stability of Pluriclosed and Generalized Ricci solitons.
method Analyzes the second variation of generalized Einstein--Hilbert functional and infinitesimal deformations.
result Stability of the flows and solitons under specific conditions.
Study cohomologies of complex manifolds with symplectic forms and their stability.
problem Analyzing cohomologies of complex manifolds with symplectic forms.
method Investigate the Hard Lefschetz Condition on Dolbeault cohomology groups using a double complex.
result Stability of the -Lemma under small deformations of but not under complex structure.
The paper studies stability of CR structures on compact manifolds.
problem Stability of CR structures on compact manifolds.
method Smooth deformations and projective embeddings.
result Nearby structures still admit projective CR embeddings.
The abstract presents power series proofs for local stabilities of Kähler and balanced structures.
problem Local stabilities of Kähler and balanced structures on complex manifolds.
method Power series method applied to a natural map of complex differential forms.
result New local stability theorems for balanced structures and p-Kähler structures.
Compactifies stability space for category, introducing -deformed rational numbers.
problem Stability conditions in triangulated categories and their compactifications.
method Embedding into an infinite-dimensional projective space, using braid group action.
result Two orbits in the boundary correspond to -deformed rational numbers.
The paper explores harmonic maps and their stability, proving key properties and conditions.
problem Existence and stability of harmonic maps between Riemannian manifolds.
method Analysis of energy functional, construction of harmonic maps, and stability conditions.
result Conditions for the stability of harmonic maps and their instability from compact manifolds.
Study deformed Hermitian-Yang-Mills equation on complex projective space blowup.
problem Solving the deformed Hermitian-Yang-Mills equation on complex projective space blowup.
method Expressed the equation as an ODE and solved it using combinatorial methods under an algebraic stability condition.
result Evidence supporting a conjecture on general compact Kahler manifolds.
Study categorizes Vaisman manifolds with vanishing first Chern class and finds canonical metrics.
problem Characterizing Vaisman manifolds with vanishing first Chern class.
method Categorization into three types based on Bott-Chern class sign, showing canonical metrics, quasi-regularity, stability, and automorphism group behavior.
result Vaisman manifolds with non-positive Bott-Chern class admit canonical metrics and are stable under deformations.
This paper concerns with deformations of noncompact complex hyperbolic manifolds (with locally Bergman metric), varieties of discrete representations of their fundamental groups into and the problem of (quasiconformal) stability of deformations of such groups and manifolds in the sense of L.Bers and D.Sulliva…
Special Hermitian metricsmath.DG
Study on special Hermitian metrics and their stability.
problem Existence and stability of Hermitian metrics with specific properties.
method Analysis of Hermitian metrics with $∂ar{∂}ω^k=0$ for to .
result Stability of metrics at blow-up and deformations.
New examples of deformed Hermitian-Yang-Mills connections found.
problem Constructing deformed Hermitian-Yang-Mills connections on manifolds.
method Constructed first higher rank, irreducible deformed Hermitian-Yang-Mills connections in both small and large radius regimes.
result Existence of solutions with any possible angle and ruling out some stability conditions.
The paper examines the stability of a specific flow on complex manifolds.
problem Stability of line bundle mean curvature flow on complex manifolds.
method Analyzes the convergence of the line bundle mean curvature flow to a deformed Hermitian-Yang-Mills metric.
result The flow converges exponentially to the deformed Hermitian-Yang-Mills metric in the sense.
In this article, we introduce a new method (based on Perelman's lambda-functional) to study the stability of compact Ricci-flat metrics. Under the assumption that all infinitesimal Ricci-flat deformations are integrable we prove: (A) a Ricci-flat metric is a local maximizer of lambda in a C^2,alpha-sense iff its Lichne…
Unified framework connects deformation theory and derived categories for multiparameter persistence.
problem Algebraic complexity of multiparameter persistence modules hinders classification, stability, and interpretability.
method Combines deformation theory and derived categories to study multiparameter persistence geometrically.
result Unified conjecture relating interleaving distance to derived convolution metrics established.