arXiv research

Surveying stability of klt singularities with new solutions.

Study shows minimizing the norm of the ERM solution stabilizes kernel ridge-less regression.

Stability inequalities for specific solutions in high dimensions.

Stability and Hölder continuity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds.

Paper addresses stability in multi-asset American option pricing.

Stable saddle solutions found for specific dimensions of the Allen-Cahn equation.

Study on linear stability of Schwarzschild spacetime using harmonic gauge.

We study existence, uniqueness and stability of radial solutions of the Lane-Emden-Fowler equation $-Δ_g u=|u|^{p-1}u$ in a class of Riemannian models $(M,g)$ of dimension $n\ge 3$ which includes the classical hyperbolic space $\mathbb H^n$ as well as manifolds with sectional curvatures unbounded below. Sign properties…

We study constant mean curvature Lorentzian hypersurfaces of $\mathbb{R}^{1,d+1}$ from the point of view of its Cauchy problem. We completely classify the spherically symmetric solutions, which include among them a manifold isometric to the de Sitter space of general relativity. We show that the spherically symmetric s…

Stability results for complex Monge-Ampère equations in various classes.

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

We consider graphical solutions to mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature: If another solution is initially close to the cone at infinity, then the difference to the homothetically expanding solution becomes small for large…

We establish various stability results for solutions of complex Monge-Ampère equations in big cohomology classes, generalizing results that were known to hold in the context of Kähler classes.

Paper presents a novel method to assess boundedness and stability of nonlinear systems with variable delays.

reval package selects best clustering solutions via stability-based validation.

Schwarzschild black hole stability proven using a new gauge.

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates.

Study on self-similar solutions of supercritical Fujita equation, proving entropy and energy gap.

Derives interior estimates for solutions of a generalized Abreu Equation in polytopes.

Stability of specific solitons proven in higher dimensions.

Future stability of FLRW solutions in expanding 3D space is shown for compact perturbations.

Paper develops a new geometric framework for Kerr stability.

Paper proves stability of solutions for specific hyperbolic systems.

We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear stability, we turn our attention to left-invariant soliton metrics on (non-compac…

Develops harmonic metrics for Hull-Strominger system stability.

Stability of singularity formation in Yang-Mills fields in higher dimensions.

The paper introduces a new method to assess system stability using torsion of state trajectories.

Analytic solutions found for a financial market model with traders.

Proves stability of charged black holes with small charge.

We prove stability of solutions of the complex Monge-Ampère equation on compact Hermitian manifolds, when the right hand side varies in a bounded set in $L^p, p>1$ and it is bounded away from zero. Such solutions are shown to be Hölder continuous. As an application we extend a recent result of Székelyhidi and Tosatti o…

In this paper, we formulate the notion of the $\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\mathcal{F}$-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's res…

Modeling financial systemic risk with optimal control theory for stability.

Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and asymptotic stability, modulo smooth finite-dimensional center manifolds, of certain R^{N}…

Paper solves PDEs for optimal investment strategies in volatile markets.

The paper proves rigidity of a specific 4D Ricci flow solution.

Study on combustion theory solutions, proving nondegeneracy and stability in limit.

Study on stability and continuity of solutions to complex Monge-Ampère equations on compact Hermitian manifolds.

Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.

Study on future stability of FLRW spacetime solutions with decelerated expansion.

Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.

The paper proves stability of a blowup solution for Yang-Mills heat flow.

Stability proven for complex equations on Kähler manifolds.

Study proves stability and uniqueness for a specific type of flow.

Study proves stability of big bang singularity in complex system.

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic sp…

VL finds flatter solutions at edge of stability, matching theory with practice.

Researchers prove stability of black holes with positive cosmological constant.

New LP method recovers MAP solution from noisy stable instances.