Study of holomorphic triples on surfaces leads to Vafa-Witten invariants.
problem Understanding moduli spaces of holomorphic triples on surfaces.
method Studied moduli space of holomorphic triples with Schmitt stability condition, observing perfect deformation-obstruction theory for large stability parameters.
result Connection between higher rank flag sheaves and Vafa-Witten theory on threefolds.
We consider constant mean curvature 1 surfaces in R3 arising via the DPW method from a holomorphic perturbation of the standard Delaunay potential on the punctured disk. Kilian, Rossman and Schmitt have proven that such a surface is asymptotic to a Delaunay surface. We consider families of such potentials p…
In the literature, two approaches to the Weierstrass representation formula using spinors are known, one explicit, going back to Kusner & Schmitt, and generalized by Konopelchenko and Taimanov, and one abstract due to Friedrich, Bayard, Lawn and Roth. In this article, we show that both points of view are indeed equival…
The paper extends Weierstrass representation to non-minimal conformal immersions.
problem Understanding conformal immersions of Riemann surfaces into 3D space.
method Generalizing Weierstrass representation to arbitrary conformal immersions and studying spin structures and spinors.
result Immersions give rise to spin structures and spinors, allowing for new ways to study the immersions.
A crucial challenge in image-based modeling of biomedical data is to identify trends and features that separate normality and pathology. In many cases, the morphology of the imaged object exhibits continuous change as it deviates from normality, and thus a generative model can be trained to model this morphological con…
Evaluating human brain potentials during watching different images can be used for memory evaluation, information retrieving, guilty-innocent identification and examining the brain response. In this study, the effects of watching images, with different levels of familiarity, on subjects' Electroencephalogram (EEG) have…
In this chapter (Chapter V) we present several results which demonstrate a close connection and useful exchange of ideas between graph theory and knot theory. These disciplines were shown to be related from the time of Tait (if not Listing) but the great flow of ideas started only after Jones discoveries. The first dee…
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.
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.
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.
In this work we study properties of stability and non-stability of harmonic maps under the homogeneous Ricci flow. We provide examples where the stability (non-stability) is preserved under the Ricci flow and an example where the Ricci flow does not preserve the stability of an harmonic map.
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.
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.
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.
In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.
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.
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.
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.
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.
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. We show that uniform K-stability is a Zariski open condition in Q-Gorenstein families of Q-Fano varieties. To prove this result, we consider the behavior of the stability threshold in families. The stability threshold (also known as the delta-invariant) is a recently introduced invariant that is known to detect the K-s…
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.
We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that uniform K-stability is equivalent to β-invariant having a positive lower bound. Then we study the relation between optimal destabilization conjecture and the conjectural equivalence between uniform K-stability and K-stabilit…
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.
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.
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.
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.
Stability theorem for concordance embeddings with applications.
problem Stability of concordance embeddings.
method Proving a stability theorem.
result Various applications to diffeomorphisms and homeomorphisms.
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. Equivalence proven between algebraic stability and geometric stability.
problem Equivalence of algebraic and geometric stability criteria.
method Algebraic proof of equivalence, existence and uniqueness of minimal centers.
result Existence and uniqueness of minimal optimal destabilizing centers.
Surveying stability of klt singularities with new solutions.
problem Stability of klt singularities.
method Survey and solution of the stable degeneration conjecture.
result Solution to the stable degeneration conjecture.
Stabilization operation for high-dimensional contact manifolds, proving many links are non-simple.
problem Understanding the structure and properties of high-dimensional contact manifolds.
method Definition and proof of stabilization operation for codimension 2 contact submanifolds in dim≥5 contact manifolds. result Many transverse links are non-simple.
Accelerated gradient method's stability deteriorates exponentially with steps.
problem Algorithmic stability of Nesterov's accelerated gradient method.
method Analysis of two notions of algorithmic stability for Nesterov's accelerated gradient method.
result Stability of Nesterov's accelerated method deteriorates exponentially with the number of gradient steps.
Study stabilizers of complex hyperbolic triangle groups, finding generators and signatures.
problem Understanding the stabilizers of complex hyperbolic triangle groups.
method Explicit generators and signatures of stabilizers computed for each group orbit of mirrors.
result Explicit generators and signatures of stabilizers for some triangle groups.
Stability results for complex Monge-Ampère equations in various classes.
problem Stability of solutions to complex Monge-Ampère equations.
method Weak stability results followed by Ck,α stability proofs. result Proves stability of solutions in relative full mass classes and on quasi-projective varieties.