arXiv research

Equivalence proven between algebraic stability and geometric stability.

Geometric invariant theory introduces stability conditions mirroring abelian category theory.

Geometric stability predicts steerability and detects drift in language models.

Boosting framework for vector-valued prediction with geometric stability.

Stability results for geometric equations in warped product spaces.

Constructs a moduli space for PDEs, linking stability to geometric metrics.

Characterizes geometric actions on graphs with flexible stabilizers.

Geometric stability measures neural network robustness, distinguishing from similarity metrics.

In this note, we shall show that the Chow-stability and the Hilbert-stability in GIT asymptotically coincide.

Schoen-Yau's zero mass theorem stability remains an open question.

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string the…

Unified treatment of stability problems in geometry and analysis.

We prove a general result about the stability of geometric flows of "closed" sections of vector bundles on compact manifolds. Our theorem allows to prove a stability result for the modified Laplacian coflow in G2-geometry introduced by Grigorian and for the balanced flow introduced by the authors in a previous paper.

New proof of Schwarzschild stability using geometric gauge.

Decomposes J-energy into simpler intersection numbers for stability analysis.

Adapts Stein's method for geometric inequalities, addressing boundary terms.

Neural nets learn robust geometric data representations.

Study higher rank deformed Hermitian-Yang-Mills equations for stable vector bundles.

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.

Study shows how to reduce data needed for learning under geometric constraints.

In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave equations satisfied by the curvatures are derived. The relation of hypergeometric flo…

The paper analyzes harmonic maps to flat model spaces to prove geometric stability of the positive mass theorem.

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

A powerful mathematical method for the investigation of the properties of dynamical systems is represented by the Kosambi-Cartan-Chern (KCC) theory. In this approach the time evolution of a dynamical system is described in geometric terms, treating the solution curves of a dynamical system by geometrical methods inspir…

We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal smooth hypersurface section stabilize in the completed Grothendieck ring of variet…

The paper tackles scalar curvature on manifolds conformal to tori, proving stability under certain conditions.

Flexible approach for normal approximations in geometric and topological statistics.

The study of gyration stability in projective planes.

Study stability of Einstein manifolds with boundary.

Survey explores geometric aspects of policy optimization in control systems.

Study on spectral stability of an embedded annulus under curve shortening and Ricci flows.

We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kaehler metric. This generalises conjectures by Yau, Tian and Donaldson which relate to the case of Kaehler-Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates thi…

Study geometric flow on curves with positive torsion, finding stationary solutions and their stability.

The paper proves geometric inequalities and their stabilities for curves in hyperbolic space.

Study on deformation of weighted scalar curvature, proving geometric results and stability.

Geometric interpretation of Fock-Goncharov positivity and disk stabilization in symmetric space.

Surveying progress on deformed Hermitian-Yang-Mills equation and its connections to stability.

In this paper we present a geometric control law for position and line-of-sight stabilization of the nonholonomic spherical robot actuated by three independent actuators. A simple configuration error function with an appropriately defined transport map is proposed to extract feedforward and proportional-derivative cont…

GCNs converge and remain stable on large random graphs, revealing geometric insights.

The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by t…

Geometrically classifies total stability spaces for Dynkin diagrams.

Stability of biharmonic maps in critical dimension proven.

Blowups of Kähler manifolds with extremal metrics inherit such metrics under stability conditions.

We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results of existence of Kahler-Einstein metrics with cone singularities.

Graph braid groups' complexity stabilizes for most graphs.

Study on stability in discretized hydrodynamics model.

From the work of Dervan-Keller, there exists a quantization of the critical equation for the J-flow. This leads to the notion of J-balanced metrics. We prove that the existence of J-balanced metrics has a purely algebro-geometric characterization in terms of Chow stability, complementing the result of Dervan-Keller. We…

Survey on stability of Minkowski spacetime in relativity.