Stability of PDEs linked to vector fields on manifolds.
problem Stability of solutions to differential equations involving vector fields.
method Analyzes Hyers-Ulam stability for global differential equations.
result Stability of solutions to the differential equation Vy=λy+f. Equivalence proven between divisorial stability and quotient log divisorial stability.
problem Equivalence of divisorial stability and log divisorial stability under finite group actions.
method Interpolation technique and equivariant divisorial stability construction.
result Equivariant divisorial stability of a polarized variety is equivalent to log divisorial stability of its quotient.
Study on stability of harmonic maps under Ricci flow.
problem Stability of harmonic maps under Ricci flow.
method Analysis of stability and non-stability properties.
result Examples of preserved and non-preserved stability under Ricci flow.
Introduces stability conditions for polarized varieties, linking to K-stability.
problem Stability conditions for polarized varieties.
method Analogue of Bridgeland's stability for polarized varieties, Z-stability, Z-critical Kähler metrics.
result Polarized varieties with certain stability conditions admit Z-critical Kähler metrics.
Proves criteria for uniform K-stability of log Fano pairs.
problem Determining conditions for uniform K-stability of log Fano pairs.
method Analyzes criteria and proves equivalence to β-invariant having a positive lower bound.
result Uniform K-stability is equivalent to β-invariant having a positive lower bound.
Shows uniform K-stability is open in Q-Gorenstein families of Q-Fano varieties.
problem Detecting uniform K-stability in families of Q-Fano varieties.
method Examined the behavior of the stability threshold in families and showed it is lower semicontinuous.
result Uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties.
Introduces valuative stability for polarised varieties, equivalent to K-stability.
problem Characterizing K-stability for polarised varieties.
method Introduces valuative stability, equivalent to K-stability for test configurations with integral central fibre.
result Equivalence of valuative stability and K-stability for polarised varieties.
The homology groups of many natural sequences of groups {Gn}n=1∞ (e.g. general linear groups, mapping class groups, etc.) stabilize as n→∞. Indeed, there is a well-known machine for proving such results that goes back to early work of Quillen. Church and Farb discovered that many sequ…
We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional F. The other one is a dynamical stability and it refers to a convergence of a Ricci flow starting at any metric in a neighbourhood of a considere…
Decomposes J-energy into simpler intersection numbers for stability analysis.
problem Analyzing J-stability in algebraic geometry.
method Proves a decomposition formula for J-energy and shows equivalence of stability conditions.
result Equivalence of J-stability and K-stability for surfaces under pseudoeffective conditions.
Paper discusses K-stability of pairs and its implications.
problem K-stability of pairs
method Analyzes stable pairs and proves implications.
result K-stability implies CM-stability.
Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.
problem Understanding max- and min-stability in stochastic dominance.
method Representation theorem for functionals satisfying max-stability, combining max- and min-stability to define Lambda-quantiles.
result New characterizations of functionals, including Lambda-quantiles, in finance and political science.
Study on stability of hyperkähler flow in 4-manifolds.
problem Stability of hyperkähler flow in 4-manifolds.
method Extending results from mean curvature flow for minimal surfaces to hyperkähler flow.
result Obtained a dynamic stability theorem for hyperkähler flow.
The paper introduces new metrics and stability criteria for complex manifolds.
problem Stability conditions for complex manifolds and metrics.
method Quantization of the J-flow, J-balanced metrics, Chow stability, uniform stability criteria.
result Existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability.
For a polarized algebraic manifold (X,L), let T be an algebraic torus in the group of all holomorphic automorphisms of X. Then strong relative K-stability will be shown to imply asymptotic relative Chow-stability. In particular, by taking T to be trivial, we see that asymptotic Chow-stability follows from stron…
Introduces new stability concept for Fano fibrations.
problem Stability of Fano fibrations with singularities.
method Introduces f-stability and shows its implications. result Fibered semi log canonical singularities are restricted.
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.
Solves modified conjecture for Fano manifolds using Ding stability.
problem Finding Kähler-Einstein metrics on Fano manifolds.
method Interprets Ding semistability and solves modified conjecture.
result Solves modified conjecture for coupled Kähler-Einstein metrics on Fano manifolds.
This paper enhances stability selection by evaluating overall results robustness and identifying optimal regularization values.
problem Improving the robustness and reliability of high-dimensional variable selection.
method Developed a stability estimator to evaluate stability of stability selection results, calibrating key parameters.
result Identified optimal regularization value and improved stability of variable selection.
This work explores the trade-offs between stability and accuracy in statistical estimation.
problem Understanding the statistical cost of algorithmic stability.
method Statistical decision-theoretic perspective, focusing on worst-case and average-case stability.
result Optimal stable estimators for mean estimation and regression settings are developed, revealing trade-offs between stability and accuracy.
The paper examines stability of harmonic and symphonic maps with forms and potentials.
problem Stability of harmonic and symphonic maps with forms and potentials.
method Analyzes stability of F-harmonic and F-symphonic maps with forms and potentials. result Stability conditions for harmonic and symphonic maps are established.
In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.
We study the stability of non compact steady and expanding gradient Ricci solitons. We first show that strict linear stability implies dynamical stability. Then we give various sufficient geometric conditions ensuring the strict linear stability of such gradient Ricci solitons.
New stability measures for similar features improve feature selection accuracy.
problem Existing stability measures fail to distinguish similar features in highly correlated datasets.
method Introduce new adjusted stability measures that consider feature similarities.
result One new stability measure considers highly similar features as interchangeable.
The paper analyzes how stacking improves model stability.
problem Lack of theoretical insight into how stacking works.
method Stability analysis of learning algorithms, focusing on hypothesis stability.
result The hypothesis stability of stacking is a product of base models and combiner.
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.
Surveying Morse boundaries and stability results.
problem Understanding Morse boundaries and their stability.
method Review of existing literature.
result Compilation of known results on Morse boundaries and stability.
Study links K-stability of certain surfaces to binary forms, proving stability and non-stability conditions.
problem Investigating K-stability of specific del Pezzo surfaces.
method Relating K-stability to GIT stability of binary forms, proving stability and non-stability conditions.
result K-polystability and non-K-stability of quasi-smooth hypersurfaces.
New stability results for configuration space cohomology.
problem Characterizing manifolds with stable cohomology of configuration spaces.
method Analyzing the cohomology of configuration spaces of manifolds, distinguishing between strong and shifted stability.
result Characterization of manifolds with stable cohomology after a shift of degree.
Study strict stability of cones with isolated singularities.
problem Stability of cones with isolated singularities.
method Analyzes special Lagrangian and coassociative cones, provides examples for the complex case.
result Proves strict stability for special Lagrangian and coassociative cones.
Extends Minkowski stability proof to minimal decay assumptions.
problem Global stability of Minkowski spacetime with minimal decay.
method Extends Christodoulou-Klainerman's proof to minimal decay assumptions.
result Exterior stability of Minkowski holds with borderline decay.
We show that if a contact open book (Σ,h) on a (2n+1)-manifold M (n≥1) is induced by a Lefschetz fibration π:W→D2, then there is a one-to-one correspondence between positive stabilizations of (Σ,h) and \emph{positive stabilizations} of π. More precisely, any positive stabilization of (Σ,h) is in…
Stability conditions on K3 surfaces are linked to the masses of spherical objects.
problem Determining stability conditions on K3 surfaces.
method Using the masses of spherical objects and lax stability conditions associated to spherical bundles.
result Stability conditions on K3 surfaces are determined by the masses of spherical objects up to a natural C-action. Paper relaxes stability and generalization assumptions for SGD.
problem Stability and generalization for SGD under restrictive assumptions.
method Introduces on-average model stability and develops novel bounds.
result First-ever-known fast bounds in low-noise setting using stability approach.
The study provides criteria for K-stability of Fano varieties using anticanonical Q-divisors.
problem Determining K-stability of Fano varieties.
method Applying Li and the first author's theorem, proposing and proving conditions related to anticanonical Q-divisors.
result Proposed condition sufficient for K-stability of Fano varieties, related to Berman-Gibbs stability.
Stability of chiral rings in N=1 theories linked to K-stability of X.
problem Understanding the stability of chiral rings in N=1 theories.
method Introducing test chiral rings and generalized maximization, studying N=1 field theory derived from D3 branes probing a three-fold singularity X.
result K-stability of X is equivalent to the stability of chiral ring of the corresponding field theory.
New stability theorem for nonorientable surfaces mapping class groups.
problem Stability of homology groups of mapping class groups of nonorientable surfaces.
method Galatius--Kupers--Randal-Williams framework of cellular E2-algebras. result New best known stability range for homology of nonorientable surfaces.
The study examines the stability of Engel-like structures in higher dimensions.
problem Stability of Engel-like distributions in higher dimensions.
method Motivated by Cartan prolongation of contact manifolds, the article introduces a higher-dimensional analogue of Engel structures and investigates their stability.
result Generalizes Gray-type stability to Engel manifolds in higher dimensions.
The paper explores how the cohomology of certain space arrangements stabilizes as the number of subspaces increases.
problem Stability of cohomology groups of complements of linear subspace arrangements.
method Representation stability in the context of cohomology groups, focusing on arrangements invariant under permutation of coordinates.
result Bounds on stabilization and alternative proof for the stabilization of cohomology groups.
The paper proves stabilization in hypersurface sections using Grothendieck rings and probabilistic methods.
problem Stabilization of configuration spaces and Hodge Euler characteristics for hypersurface sections.
method Geometric and cohomological stabilization, probabilistic interpretation, Grothendieck ring analysis.
result Explicit formulas for stable values of Hodge Euler characteristics and point counts.
Proves uniform K-stability is open in Kähler cone.
problem Stability of Kähler metrics in complex geometry.
method Introduced new norm on test configurations and estimates for non-archimedean energy functionals.
result Uniform K-stability is an open condition in the Kähler cone.
New stability thresholds detect K-stability in Fano manifolds.
problem Detecting K-stability in Fano manifolds.
method Introducing new stability thresholds and studying geodesic rays in Kähler potentials.
result New entropy functional relates to radial entropy functional.
Stability of Wasserstein spaces under various convergence types.
problem Stability and finiteness of Wasserstein spaces over singular and non-singular spaces.
method Gromov--Hausdorff convergence and equivariant Gromov--Hausdorff convergence.
result Analogue of Perelman's stability theorem on Wasserstein spaces.
KCRL learns stable policies for nonlinear systems with formal guarantees.
problem Lack of stabilization guarantees in RL methods for safety-critical systems.
method KCRL uses Krasovskii's Lyapunov functions as a stability constraint and a primal-dual approach to learn stabilizing policies.
result KCRL guarantees learning a stabilizing policy in a finite number of interactions.
New stability criteria for Fano varieties using generalized b-divisors.
problem Characterizing uniform K-stability in Fano varieties. method Introducing a new function ildeδ and formalism for K-stability, proving stability conditions for Kähler-Einstein metrics. result Existence of a unique Kähler-Einstein metric implies uniform D-log K-stability when ildeδ(D)>1. The cohomology of complex irreducible polynomials stabilizes with degree or variables.
problem Understanding the cohomology of complex irreducible polynomials.
method Proving homological stability in cohomology as degree or variables increase.
result Cohomology stabilizes with respect to both degree and number of variables.
The paper proves stability of Ricci de Turck flow near conical singularities.
problem Stability of Ricci de Turck flow near conical singularities.
method Constructing a Ricci de Turck flow starting close to a Ricci-flat metric with isolated conical singularities.
result The flow converges to a singular Ricci-flat metric under certain conditions.
Stabilizes linear models for clinical adoption by detecting feature correlations.
problem Instability of sparse high-dimensional models hinders clinical adoption.
method Regularizes latent correlation in features using an autoencoder network.
result Significant improvement in feature stability and model estimation stability.