arXiv research

We show that if a contact open book $(Σ,h)$ on a $(2n+1)$-manifold $M$ ($n\geq1$) is induced by a Lefschetz fibration $π:W \to D^2$, 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…

Controller stabilizes spherical robot's position and line-of-sight.

New method improves feature selection by integrating stability paths.

Proves stability of gravitational instantons, proving operator positivity.

Stability of positive mass theorem for hyperbolic manifolds studied.

Stability theorem for axisymmetric manifolds with nonnegative scalar curvature.

Stability of positive mass theorem for hyperbolic graphs proven.

We prove the weak stability of expanding gradient Ricci solitons with positive curvature operator and quadratic curvature decay at infinity.

New method embeds dynamic networks with stability for node behavior.

The study examines rigidity and stability of gradient estimates on surfaces and manifolds.

Paper proves stability of positive mass theorem for specific types of manifolds.

Study on stability of Positive Mass Theorem using Inverse Mean Curvature Flow.

Stability of positive mass theorem proven under Ricci curvature bounds.

Sharp stability estimate for tensor tomography in non-positive curvature.

Paper proposes a new approach to stabilize GAN training by treating generated data as unlabeled.

The paper proves stability of a quasi-local positive mass theorem for graphical hypersurfaces.

Alternative proof for 2-bridge knots' bridge positions.

New stability criteria for vector bundles linked to Hermite-Einstein geometry.

Study on Einstein manifolds linking stability and rigidity.

The paper proves stability of the positive mass theorem using intrinsic flat convergence.

Generalized stability theorem for compact manifolds with boundary.

Stability Selection improves structured variable selection but requires careful tuning.

Introduces a new equation for complex surfaces, proving stability and inequalities.

Stability and rigidity of Ricci-flat ALE manifolds proven.

The study proves stability of the positive mass theorem for Kähler manifolds.

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

The paper proves stability for Einstein metrics with special twisted spinors.

Oil prices affect Russian banks' stability, with negative impacts from decreases.

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

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

The study examines stability and instability of Poincaré-Einstein metrics using Ricci flow.

Proves criteria for uniform K-stability of log Fano pairs.

Bridge positions of handlebody-knots are equivalent when stable.

Stability of black holes proven in full subextremal range with positive cosmological constant.

Extends classical stability results to new geometric settings.

Study on stability of quaternion-Kähler manifolds using eigenvalue estimates.

Proves a conjecture about manifolds and scalar curvature.

We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability fo…

Leon Green obtained remarkable rigidity results for manifolds of positive scalar curvature with large conjugate radius and/or injectivity radius. Using $C^{k,α}$ convergence techniques, we prove several differentiable stability and sphere theorem versions of these results and apply those also to the study of Einstein m…

Let $\mathcal{L}$ be a knot with a fixed positive crossing and $\mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology $\widehat{\text{HFK}}(\mathcal{L}_n)$ `stabilizes' as $n$ goes to infinity. This categorifies a similar stabilization phenomenon of …

Stability of the utility maximization problem with random endowment and indifference prices is studied for a sequence of financial markets in an incomplete Brownian setting. Our novelty lies in the nonequivalence of markets, in which the volatility of asset prices (as well as the drift) varies. Degeneracies arise from …

Study bounds outer surfaces in small mass geometrostatic manifolds.

We show that the Kähler-Ricci flow on a manifold with positive first Chern class converges to a Kähler-Einstein metric assuming positive bisectional curvature and certain stability conditions.

Paper defines new stability and metrics for complex spaces.

We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.

We show that any non-minimal bridge decomposition of a torus knot is stabilized and that $n$-bridge decompositions of a torus knot are unique for any integer $n$. This implies that a knot in a bridge position is a torus knot if and only if there exists a torus containing the knot such that it intersects the bridge sphe…

Study stability of pseudo-Kähler and neutral Calabi-Yau manifolds, finding stability in 2D but failing in higher dimensions.

Stability of Einstein metrics under Ricci iteration studied.