相关论文: The Urysohn sphere is oscillation stable

We give an different proof of our result computing the stable homology of dihedral group Hurwitz spaces. This proof employs more elementary methods, instead of higher algebra.

In a Riemannian manifold with a smooth positive function that weights the associated Hausdorff measures we study stable sets, i.e., second order minima of the weighted perimeter under variations preserving the weighted volume. By assuming…

Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus…

Assuming the stability of soliton surfaces of vanishing Ricci sectional curvature of soliton metric in the nonholonomic frame, we find a solution for the metric in the approximation of weak constant torsion curves with constant Frenet…

Numerical evidence is presented for the existence of a new family of static, globally regular `cosmological' solutions of the spherically symmetric Einstein-Yang-Mills-Higgs equations. These solutions are characterized by two natural…

Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review describes a unified theoretical framework, the loop space…

In this paper we discuss the stability of geodesic spheres in $\mathbb{S}^{n+1}$ under constrained curvature flows. We prove that under some standard assumptions on the speed and weight functions, the spheres are stable under perturbations…

Let $ D$ be a bounded open subset of $\mathbb R^n$ with $|\partial D| < \infty$ and let $x_0 $ be a point of $D$. We introduce a new parameter, that we call Kuran gap of $\partial D$ w.r.t. $x_0$. Roughly speaking, this parameter, denoted…

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…

Spherically symmetric solutions in F(R) theories in astronomical systems with rising energy density are studied. The range of parameters is established for which the flat space-time approximation for the background metric is valid. For the…

Exact particle-like static, spherically and/or cylindrically symmetric solutions to the equations of interacting scalar and electromagnetic field system have been obtained. We considered Freedman-Robertson-Walker (FRW) space-time as an…

Two metric perturbations in Einstein-Cartan cosmology are examined.The first case is the scalar mode perturbation of de Sitter metric in Einstein-Cartan cosmology.In this case small perturbations of de Sitter metric shows that this metric…

We study the stability of capillary hypersurfaces in a unit Euclidean ball. It is proved that if the mass center of the generalized body enclosed by the immersed capillary hypersurface and the wetted part of the sphere is located at the…

We extend to Minkowski spaces the classical result of Barbosa and do Carmo [1] that characterizes the euclidean sphere as the unique compact stable CMC hypersurface of $\mathbb R^n$. More precisely, if $K$ is a smooth convex body in…

This survey deals with two closely connected topics: first, the stability of Einstein metrics under the Einstein-Hilbert functional, and second, their deformation theory and the study of the moduli space of Einstein metrics on a compact…

Using an approach similar to arXiv:2409.15460, we give a new proof of the nonlinear stability of de Sitter space as a solution to the Einstein vacuum equations with positive cosmological constant in $n+1$ dimensions, with $n\geq3$. Using…

We study the Einstein-Lichnerowicz constraints system, obtained through the conformal method when addressing the initial data problem for the Einstein equations in a scalar field theory. We prove that this system is stable with respect to…

The mixed Christoffel problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, all but one of them are fixed. We consider the case in which the…

The paper is concerned with the Einstein equations for a spherically symmetric static distribution of anisotropic matter. The equations are cast into a system of Fuchsian type ODE for certain scalar invariants of the strain. And then the…

We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…