Related papers: Stability between foliations in general relativity
Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…
The presence of two compatible Hamiltonian structures is known to be one of the main, and the most natural, mechanisms of integrability. For every pair of Hamiltonian structures, there are associated conservation laws (first integrals).…
We solve the spacelike, spherically symmetric, constant mean curvature hypersurfaces in the maximally extended Reissner-Nordstrom spacetime with the charge smaller than the mass. Based on these results, we construct constant mean curvature…
We study moduli space stabilization of a class of BPS configurations from the perspective of the real intrinsic Riemannian geometry. Our analysis exhibits a set of implications towards the stability of the D-term potentials, defined for a…
In this paper, we study planar polygonal curves from the variational methods. We show an unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first…
Filamentary structures are ubiquitous in astrophysics and are observed at various scales. On a cosmological scale, matter is usually distributed along filaments, and filaments are also typical features of the interstellar medium. Within a…
The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…
In this paper, we study submanifolds with constant $r$th mean curvature $S_r$. We investigate, the stability of such submanifolds in the case when they are leaves of a codimension one foliation. We also generalize recent results by Barros -…
This paper extends the results of [GLS24], where the existence of a constant harmonic mean curvature foliation was established in the setting of a 3-dimensional asymptotically Schwarzschild manifold. Here, we generalize this construction to…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
In this paper, we study stability for harmonic foliations on locally conformal K\"ahler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact…
A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
The linear stability of a stratified shear flow for smooth density profiles is studied. This work focuses on the nature of the stability boundaries of flows in which both Kelvin-Helmholtz and Holmboe instabilities are present. For a fixed…
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
We investigate the classical stability of the higher-dimensional Schwarzschild black holes against linear perturbations, in the framework of a gauge-invariant formalism for gravitational perturbations of maximally symmetric black holes,…
This article deals with the irreducible components of the space of codimension one foliations in a projective space defined by logarithmic forms of a certain degree. We study the geometry of the natural parametrization of the logarithmic…
We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust…
We consider the nonlinear Schr\"odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard…