Stability of capillary hypersurfaces with higher order mean curvature.
problem Stability of capillary hypersurfaces with constant higher order mean curvature.
method Generalization of classical stability theory for capillary hypersurfaces.
result Results on stability for capillary hypersurfaces with higher order mean curvature.
The study shows stability of neckpinch singularities in mean curvature flows.
problem Stability of neckpinch singularities in mean curvature flows.
method Analysis of mean curvature flow and perturbations.
result Stability of neckpinch singularities in mean curvature flows.
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.
We propose a notion of stability for constant k-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means of the variational problem. Our approach led us to work with two different stabi…
Study on stability of mean curvature flow in hyperbolic space.
problem Stability of volume preserving mean curvature flow in hyperbolic space.
method Analysis of initial conditions and flow behavior in hyperbolic space.
result The flow converges exponentially to an umbilical sphere under certain conditions.
The study proves stability of various graphical translators in mean curvature flow.
problem Stability of graphical translators in mean curvature flow.
method Existence of longtime solution to mean curvature flow, dynamical stability results for various graphical translators.
result Dynamical stability of various types of graphical translators.
The paper examines the stability of a specific flow on complex manifolds.
problem Stability of line bundle mean curvature flow on complex manifolds.
method Analyzes the convergence of the line bundle mean curvature flow to a deformed Hermitian-Yang-Mills metric.
result The flow converges exponentially to the deformed Hermitian-Yang-Mills metric in the C∞ sense. The study examines stability of triharmonic hypersurfaces in space forms.
problem Stability of triharmonic hypersurfaces in space forms.
method Derivation of general stability statements, focus on specific cases of constant mean curvature in Euclidean and hyperbolic spaces, and analysis of small proper triharmonic hyperspheres and Clifford tori.
result Triharmonic hypersurfaces of constant mean curvature in Euclidean space are weakly stable with respect to normal variations, while in hyperbolic space they are stable.
Study proves stability and uniqueness for a specific type of flow.
problem Volume-preserving mean curvature flow stability and uniqueness.
method New gradient flow calibrations for volume preservation, stability estimate in distributional solutions.
result Strong solutions are calibrated and stable under certain conditions.
Paper proves stability of flow in cotangent bundle for special Lagrangian submanifolds.
problem Stability of generalized Lagrangian mean curvature flow in cotangent bundle.
method New derivative estimates to weaken initial conditions and remove curvature constraints.
result Stability of flow near special Lagrangian submanifolds in cotangent bundle.
The study extends curvature bounds to non-smooth spaces and proves stability of mean curvature.
problem Proving curvature bounds in non-smooth spaces.
method Extending results from smooth Riemannian manifolds to non-smooth RCD spaces.
result Stability of mean curvature bounds under uniform convergence.
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 find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones att…
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.
The paper proves the stability of a flow in Schwarzschild space.
problem Stability of area preserving mean curvature flow in asymptotic Schwarzschild space.
method Demonstrates existence and exponential convergence of the flow for all time.
result The flow converges to a round sphere or a constant mean curvature surface.
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 …
Paper proves stability and Dirichlet problem for translating hypersurfaces.
problem Stability and Dirichlet problem for translating hypersurfaces.
method Analyzes translating solitons in en+k, proves stability conditions, and studies Dirichlet problem. result Proves the infimum of mean curvature is zero for translating solitons and conditions for stability.
We investigate the role of the initialization for the stability of the k-means clustering algorithm. As opposed to other papers, we consider the actual k-means algorithm and do not ignore its property of getting stuck in local optima. We are interested in the actual clustering, not only in the costs of the solution. We…
Minimal Lagrangians in certain curved spaces are stable under specific flows.
problem Stability of minimal Lagrangians in Kähler-Einstein manifolds of non-positive curvature.
method Proved stability under Lagrangian mean curvature flow.
result Equivalence between linear and dynamical stability for C1-close Lagrangians. The paper examines stability of Yamabe boundary problem under perturbations.
problem Stability of Yamabe boundary problem under perturbations of mean curvature and scalar curvature.
method Analyzes stability of the Yamabe boundary problem with respect to perturbations of mean curvature and scalar curvature.
result The stability of the Yamabe boundary problem is proven under perturbations from below, but not from above.
We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random per…
Study stabilizes translating solitons in hyperbolic space for MCF.
problem Stability of translating solitons in hyperbolic space.
method Developed theory, constructed rotationally invariant translators, used avoidance principle and maximum principle.
result Horospheres are dynamically stable as radial graphical solutions to MCF.
New algorithms robustly estimate mean with near-optimal error rates.
problem Outlier robust mean estimation in high-dimensional data.
method Stability condition and iterative filtering algorithms.
result Optimal error rates with subgaussian rates for robust mean estimation.
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…
In this paper, we formulate the notion of the F-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the F-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's res…
Surface diffusion and mean curvature flows converge to stable critical sets in flat tori.
problem Stability of surface diffusion and mean curvature flows in flat tori.
method Existence and convergence of flows starting close to stable critical sets, proven for all times.
result Flows converge exponentially fast to stable critical sets in flat tori.
We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its C2-distance fro…
Paper analyzes SHB method for neural networks, proving stability, connectivity, and global convergence.
problem Theoretical understanding of SHB method for neural networks.
method Mean-field analysis of SHB dynamics related to a partial differential equation.
result SHB method converges to global optimum and exhibits stability and connectivity.
Paper controls shape stability in infinite Riemannian manifolds.
problem Characterizing optimal shapes in infinite-dimensional Riemannian manifolds.
method Uses Riemannian manifold framework and mean curvature analysis.
result Control on shape stability depends only on mean curvature.
The paper studies stability of mean-field variational inference for log-concave distributions.
problem Stability of mean-field variational inference for log-concave distributions.
method Novel approach via linearized optimal transport, lifting non-convex problem to convex optimization over transport maps.
result Dimension-free Lipschitz continuity of the MFVI optimizer with respect to the target distribution, measured in 2-Wasserstein distance.
In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.
3D metrics get scalar curvature bounds via IMCF.
problem Bounding scalar curvature for C0 metrics. method Inverse Mean Curvature Flow (IMCF) and Hawking mass monotonicity.
result Stability theorem for nonnegative scalar curvature.
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.
The paper studies the stability of volume and area preserving mean curvature flows in Schwarzschild and asymptotic Schwarzschild spaces.
problem Investigating the stability of mean curvature flows in specific spacetime geometries.
method Combining center manifold analysis with global existence results for flows near isoperimetric hypersurfaces.
result Global existence and convergence to constant mean curvature (CMC) hypersurfaces for flows in asymptotic Schwarzschild space.
Entropy regularization improves MFG learning efficiency and stability.
problem Improving Mean Field Game learning efficiency and stability.
method Entropy regularization applied to MFG with learning.
result Entropy regularization yields time-dependent policies and stabilizes convergence.
New stability conditions for ZO methods reveal unique regularization effects.
problem Understanding optimization dynamics of ZO methods in deep learning.
method Explicit step size conditions and stability bounds derived for ZO methods.
result ZO methods operate near the edge of stability, with regularization effects specific to Hessian trace vs. eigenvalue.
Paper studies stability of curved surfaces in a half-space.
problem Stability of anisotropic capillary hypersurfaces in a half-space.
method Analyzes weak stability and proves Bernstein-type theorems.
result Compact hypersurfaces are stable if and only if they are a truncated Wulff shape.
We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature surfaces immersed into certain 3-dimensional Riemannian spaces, in particular into homogeneous 3-manifolds. As an application we derive some consequences for strongly stable surfaces in such ambient spaces. M…
We study the mean curvature flow of hypersurfaces in Rn+1, with initial surfaces sufficiently close to the standard n-dimensional sphere. The closeness is in the Sobolev norm with the index greater than 2n+1 and therefore it does not impose restrictions of the mean curvature of the initial surface. W…
We present three ways to establish general stability inequalities for various classes of 2-immersions in Euclidean spaces of higher codimension
Optimism stabilizes Thompson Sampling for adaptive inference in multi-armed bandits.
problem Subtle inferential properties of Thompson Sampling under adaptive data collection.
method Introduced optimism as a key mechanism to restore stability and validity of inference.
result Suitably implemented optimism stabilizes Thompson Sampling and enables asymptotically valid Wald inference.
GNMR controls runtime stability in low-precision language model training.
problem Efficient low-precision training faces numerical risks at specific operators.
method GNMR compares gradient norms to historical means, applying bounded recovery actions.
result GNMR preserves high-fidelity quality with sparse, budgeted recovery.
New model stabilizes asynchronous LTI systems, independent of synchronous stability.
problem Stability of asynchronous LTI systems under randomization and asynchrony.
method Introduced a new model for random asynchronous LTI systems and developed a method for system identification.
result Stability of random asynchronous LTI systems is independent of synchronous stability.
In this paper we study the r-stability of closed spacelike hypersurfaces with constant r-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of r−stability through the analysis of the first eigenvalue of an operator naturally attached…
The paper examines stable CMC hypersurfaces with boundaries on parallel hyperplanes.
problem Stability of CMC hypersurfaces with free boundaries.
method Analysis and numerical computations.
result Equilibrium hypersurfaces are stable without self-intersection in all dimensions.
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.
The paper proves rigidity and stability properties of self-shrinking surfaces in 3D space.
problem Rigidity and stability of self-shrinking surfaces in R3. method Analyzing the mean curvature flow and L-index of self-shrinkers. result No stable two-dimensional self-shrinker in R3 exists without properness. A method to remove mean-shift noise from PCA using knockoffs.
problem High sensitivity of PCA to mean-shift contamination in high-dimensional data.
method Introducing knockoff mean-shift perturbation to separate and remove mean-shift components from PCA.
result The mean-shift spikes are spectrally separable from stable eigenvalues, allowing for robust PCA.