Related papers: Stable and unstable Einstein warped products
The goal of this article is to investigate complete noncompact warped product gradient Ricci solitons. Nonexistence results, estimates for the warping function and for its gradient are proven. When the soliton is steady or expanding these…
In this note we prove three rigidity results for Einstein manifolds with bounded covering geometry. (1) An almost flat manifold $(M,g)$ must be flat if it is Einstein, i.e. $\operatorname{Ric}_g=\lambda g$ for some real number $\lambda$.…
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,…
The characterization and mechanical stability of charged thin shells with spherical symmetry are analyzed in the context of Einstein-Born-Infeld theory. The study of stability is performed by considering linearized perturbations preserving…
In this paper we prove that under certain conditions in a quasi Einstein semi Riemannian warped product the fiber is necessarily a Einstein manifold. We provide all the quasi Einstein manifolds when r Bakry Emery tensor is null, the base is…
The goal of this article is to study the geometry of Bach-flat noncompact steady quasi-Einstein manifolds. We show that a Bach-flat noncompact steady quasi-Einstein manifold $(M^{n},\,g)$ with positive Ricci curvature such that its…
We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to…
We study the geometric structure of weighted Einstein smooth metric measure spaces with weighted harmonic Weyl tensor. A complete local classification is provided, showing that either the underlying manifold is Einstein, or decomposes as a…
In this paper, we compute the index and nullity for minimal submanifolds of some complex Einstein spaces. We investigate the stability of these minimal submanifolds and suggest a criterion for instability for some cases. We also compute…
We carry out a Painlev\'e analysis to find the cases where the cohomogeneity one steady Ricci soliton equation can be integrable. We concentrate on two classes of solitons: warped products and complex line bundles over a Fano K\"ahler…
It is established in [6, 14, 23] that any closed Einstein manifold with two-nonnegative curvature operator of the second kind is either flat or a round sphere. In this paper, we refine this result by relaxing the curvature condition to a…
We prove dynamical stability and instability theorems for Poincar\'{e}-Einstein metrics under the Ricci flow. Our key tool is a variant of the expander entropy for asymptotically hyperbolic manifolds, which Dahl, McCormick and the first…
We prove the instability of conformally K\"ahler, compact or ALF Einstein 4-manifolds with nonnegative scalar curvature which are not half conformally flat. This applies to all the known examples of gravitational instantons which are not…
We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrodinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin…
We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear…
We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions…
Non K\"ahler Calabi Yau theory is a newly developed subject and it arises naturally in mathematical physics and generalized geometry. The relevant geometrics are pluriclosed metrics which are critical points of the generalized Einstein…
We annnounce a proof of the fact that a K-stable Fano manifold admits a Kahler-Einstein metric and give a brief outline of the proof.
Let $ M = G/K $ be a full flag manifold. In this work, we investigate the $ G$-stability of Einstein metrics on $M$ and analyze their stability types, including coindices, for several cases. We specifically focus on $F(n) =…
We prove new isolation and stability results for Einstein manifolds in a variety of settings. Imposing conditions on the Weyl tensor, we establish new stability criteria for compact, asymptotically hyperbolic (AH) and asymptotically locally…