Related papers: K stability and stability of chiral ring

We define the relative stability threshold of a family of Fano varieties over a DVR and show that it is computed by a divisorial valuation. In the case when the special fiber is K-unstable, but the generic fiber is K-semistable, we use the…

The kink stability of self-similar solutions of a massless scalar field with circular symmetry in 2+1 gravity is studied, and found that such solutions are unstable against the kink perturbations along the sonic line (self-similar horizon).…

In this paper we generalize the neck-stability theorem of Kleiner-Lott to a special class of four-dimensional nonnegatively curved Type I $\kappa$-solutions, namely, those whose asymptotic shrinkers are the standard cylinder…

We investigate the transfer of w-stability and Clifford w-regularity from a domain D to the polynomial ring D[X]. We show that these two properties pass from D to D[X] when D is either integrally closed or it is Mori and w-divisorial.

We show that a ring R has stable range one if and only if every left unit lifts modulo every left principal ideal. We also show that a left quasi-morphic ring has stable range one if and only if it is left uniquely generated. Thus we answer…

Let A be an approximately subhomogeneous (ASH) C*-algebra with slow dimension growth. We prove that if A is unital and simple, then the Cuntz semigroup of A agrees with that of its tensor product with the Jiang-Su algebra Z. In tandem with…

Let $k$ be a field, and let $G$ be a simply connected semisimple k-group which is isotropic and contains a strictly proper parabolic $k$-subgroup $P$. Let $D$ be a discrete valuation ring which is a local ring of a smooth algebraic curve…

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…

Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology,…

A group may be considered $C^*$-stable if almost representations of the group in a $C^*$-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are $C^*$-stable or only stable with…

We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension one. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via…

We describe a procedure to compute the rational nonstable K-groups of A$\mathbb{T}$-algebras. As an application, we show that an A$\mathbb{T}$-algebra is K-stable if and only if it has slow dimension growth.

Let $k$ be a field. Then Gaussian elimination over $k$ and the Euclidean division algorithm for the univariate polynomial ring $k[x]$ allow us to write any matrix in $SL_n(k)$ or $SL_n(k[x])$, $n\geq 2$, as a product of elementary matrices.…

We use the correspondence between extremal Sasaki structures and weighted extremal Kahler metrics defined on a regular quotient of a Sasaki manifold, established by the first two authors, and Lahdili's theory of weighted K-stability in…

In previous hydrodynamical simulations, we found a mechanism for nearly circular binary stars, like Kepler-413, to trap two planets in a stable 1:1 resonance. Therefore, the stability of coorbital configurations becomes a relevant question…

We show that any $n$-dimensional Fano manifold $X$ with $\alpha(X)=n/(n+1)$ and $n\geq 2$ is K-stable, where $\alpha(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits K\"ahler-Einstein metrics and the…

The dynamics of a rigid, rotating, precessing, massive ring orbiting a point mass within the perimeter of the ring are considered. It is demonstrated that orbits dynamically stable against perturbations in three dimensions exist for a range…

Periodic orbits for the classical $\phi^4$ theory on the one dimensional lattice are systematically constructed by extending the normal modes of the harmonic theory, for periodic, fixed and free boundary conditions. Through the process, we…

We analyze classical and quantum chiral ring relations of four dimensional ${\cal N} = 1$ adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the mass deformed theory we obtain the complete on shell vacuum…

A scalar field theory with a $\chi^\dag\chi\phi$ interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard text book examples and research articles. In order to reconcile these…