arXiv research

Stability theorem for concordance embeddings with applications.

Study on stability of hyperkähler flow in 4-manifolds.

Stability results for geometric equations in warped product spaces.

Adapts a short argument to derive a stability theorem for smooth maps.

We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that …

Real analytic maps can be unstable even if infinitesimal changes are stable.

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

Stability of positive mass theorem proven under Ricci curvature bounds.

New stability theorem for nonorientable surfaces mapping class groups.

Paper proves almost all stabilizer subgroups of Thompson's group satisfy Alexander's theorem.

The article examines how many stabilizations are needed to transform 5D s-cobordisms into product cobordisms.

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

Stability of positive mass theorem for hyperbolic manifolds studied.

New stability theorem for hyperbolic metrics without volume bounds.

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

Stability of mapping spaces is shown to be related to the D-topology.

The paper finds commutator formulas for Gradient Ricci Shrinker metrics and applies them to linear stability.

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

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

Study stability of surfaces in spacetimes, proving new estimates and theorems.

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

Study on Einstein manifolds linking stability and rigidity.

We give a complete and detailed proof of Harer's stability theorem for the homology of mapping class groups of surfaces, with the best stability range presently known. This theorem and its proof have seen several improvements since Harer's original proof in the mid-80's, and our purpose here is to assemble these many a…

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is…

Abstract: Lipschitz homeomorphisms are deformed using Perelman's methods.

Generalized stability theorem for compact manifolds with boundary.

Study max- and min-stability under first-order stochastic dominance, finding new functional characterizations.

In this paper we obtain a stability theorem of generalized Kahler structures with one pure spinor under small deformations of generalized complex structures. (This is analogous to the stability theorem of Kahler manifolds by Kodaira-Spencer.) We apply the stability theorem to a class of compact Kahler manifolds which a…

We prove a version the local Reeb-Thurston stability theorem for symplectic foliations.

We give a proof of the celebrated stability theorem of Perelman stating that for a noncollapsing sequence $X_i$ of Alexandrov spaces with curvature bounded below Gromov-Hausdorff converging to a compact Alexandrov space $X$, $X_i$ is homeomorphic to $X$ for all large $i$.

Smooth compactness theorem for elasticae, except straight segments.

We consider dynamical stability for a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics. Our focus is on homogeneous metrics on non-compact manifolds. Following the program of Guenther, Isenberg, and Knopf, we define a class of weighted little Hölder spaces with certain …

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into the study of homological stability. This makes it possible to extend classical t…

The paper improves stability estimates for soap bubble theorem in curved domains.

Survey on scalar curvature stability and related questions.

New theorem shows nearly spherical manifolds can be mapped from spheres.

Simplified plat diagrams for unlink without stabilization.

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems for compact foliations in Kaehler manifolds of Edwards-Millett-Sullivan and Hollma…

Stability of Wasserstein spaces under various convergence types.

We prove a theorem on structural stability of smooth attractor-repellor endomorphisms of compact manifolds, with singularities. By attractor-repellor, we mean that the non-wandering set of the dynamics $f$ is the disjoint union of a repulsive compact subset with a hyperbolic attractor on which $f$ acts bijectively. The…

We obtain a Central Limit Theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin's Omnibus Central Limit Theorem for Fréchet means. We obtain our CLT assuming certain stability hypothesis for the cut locus, which always holds when the ma…

We prove a homological stability theorem for moduli spaces of simply-connected manifolds of dimension $2n > 4$, with respect to forming connected sum with $S^n \times S^n$. This is analogous to Harer's stability theorem for the homology of mapping class groups. Combined with previous work of the authors, it gives a cal…

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…

We give another proof of a theorem of Hatcher and Vogtmann stating that the sequence $Aut(F_n)$ satisfies integral homological stability. The paper is for the most part expository, and we also explain Quillen's method for proving homological stability.

The positive mass theorem states that the total mass of a complete asymptotically flat manifold with non-negative scalar curvature is non-negative; moreover, the total mass equals zero if and only if the manifold is isometric to the Euclidean space. Huang and Lee [2015] proved the stability of the Positive Mass Theorem…

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surface…

In this paper the stability theorem of Borkar and Meyn is extended to include the case when the mean field is a differential inclusion. Two different sets of sufficient conditions are presented that guarantee the stability and convergence of stochastic recursive inclusions. Our work builds on the works of Benaim, Hofba…