Related papers: Some isolation and stability results for Einstein …

In the article we introduce new conformal and smooth invariants on compact, oriented four-manifolds with boundary. In the first part, we show that "positivity" conditions on these invariants will impose topological restrictions on…

Let $(M^n,g)$, $n \ge 4$, be a compact simply-connected Riemannian manifold with nonnegative isotropic curvature. Given $0<l\le L$, we prove that there exists $\eps = \eps (l,L,n)$ satisfying the following: If the scalar curvature $s$ of…

In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…

In the present paper we have constructed a new relativistic anisotropic compact star model having a spherically symmetric metric of embedding class one. Here we have assumed an arbitrary form of metric function and solved the Einstein…

We have presented a new anisotropic solution of Einstein's field equations for compact star models. The Einstein's field equations are solved by using the class one condition \cite{1}. After that we constructed the physically valid…

We examine the linear stability of various configurations in Bose-Einstein condensates with sonic horizons. These configurations are chosen in analogy with gravitational systems with a black hole horizon, a white hole horizon and a…

We give an algebraic criterion for the existence of projectively Hermitian-Yang-Mills metrics on a holomorphic vector bundle $E$ over some complete non-compact K\"ahler manifolds $(X,\omega)$, where $X$ is the complement of a divisor in a…

In this paper, improving a preceding work, we obtain asymptotic polybalanced kernels associated to extremal Kaehler metrics on polarized algebraic manifolds. As a corollary, we have a stronger asymptotic relative Chow-polystability for…

We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the K\"ahler cone of any compact K\"ahler manifold, thus establishing an algebro-geometric…

$\ell$-boson stars are static, spherical, multi-field self-gravitating solitons. They are asymptotically flat, finite energy solutions of Einstein's gravity minimally coupled to an odd number of massive, complex scalar fields. A previous…

This article is the second of two in which we develop a geometric framework for analysing silent and anisotropic big bang singularities. In the present article, we record geometric conclusions obtained by combining the geometric framework…

We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key…

Let $(M,\omega)$ be a K\"ahler manifold and let $K$ be a compact group that acts on $M$ in a Hamiltonian fashion. We study the action of $K^\mathbb{C}$ on probability measures on $M$. First of all we identify an abstract setting for the…

We demonstrate a technique to generate new class of exact solutions to the Einstein-Maxwell system describing a static spherically symmetric relativistic star with anisotropic matter distribution. An interesting feature of the new class of…

This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…

This work is devoted to the study of Einstein equations with a special shape of the energy-momentum tensor. Our results continue Stepanov's classification of Riemannian manifolds according to special properties of the energy-momentum tensor…

In this paper, we study the regularity of asymptotically hyperbolic metrics with Einstein condition near boundary and Weyl curvature smooth enough in arbitrary dimension. Following Michael Anderson's method, we show that $C^{m,\alpha}$…

We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian…

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration…

We study the stability of compact pseudo-K\"ahler manifolds, i.e. compact complex manifolds $X$ endowed with a symplectic form compatible with the complex structure of $X$. When the corresponding metric is positive-definite, $X$ is K\"ahler…