In this paper a Penrose limit is constructed for type IIB $AdS_6\times S^2\times \Sigma$ supergravity solutions. These solutions are dual to five dimensional SCFTs related (p,q) brane webs, which can often be described in terms of long quiver gauge theories. The null geodesic from the localized at unique point on two Riemann surface $\Sigma$, where $AdS_6$ and $S^2$ metric factors extremal. res...

It was proved by M. Bonk, J. Heinonen and P. Koskela that the quasihyperbolic metric hyperbolizes (in the sense of Gromov) uniform metric spaces. In this paper we introduce a new metric that hyperbolizes all locally compact noncomplete metric spaces. The metric is generic in the sense that (1) it can be defined on any metric space; (2) it preserves the quasiconformal geometry of the space; (3) ...

We give a new notion of angle in general metric spaces; more precisely, given a triple a points p, x, q in a metric space (X, d), we introduce the notion of angle cone ∠pxq as being an interval ∠pxq := [∠pxq,∠ + pxq], where the quantities ∠ ± pxq are defined in terms of the distance functions from p and q via a duality construction of differentials and gradients holding for locally Lipschitz fu...

where K ≥ 1 is the least number such that there is a K-quasiconformal mapping between the marked structures X1 and X2. The mapping class group Mod(S) acts properly discontinuously and isometrically on Teich(S), thus inducing a metric dM(S)(·, ·) on the quotient moduli space M(S) := Teich(S)/Mod(S). Let π : Teich(S) → M(S) be the natural projection. The goal of this paper is to build an “almost ...

In this paper, we introduce the concepts of an inferior idempotent cone and a BID-cone b-metric space over Banach algebra. We establish some new existence theorems fixed point in setting complete spaces Some fundamental questions examples are also given.

In this article we study metric spaces which admit polynomial diameter-volume inequalities for k-dimensional cycles. These generalize the notion of cone type inequalities introduced by M. Gromov in his seminal paper Filling Riemannian manifolds. In a first part we prove a polynomial isoperimetric inequality for k-cycles in such spaces, generalizing Gromov’s isoperimetric inequality of Euclidean...

Motivated by the classical statements of Mirror Symmetry, we study certain Kähler metrics on the complexified Kähler cone of a Calabi– Yau threefold, conjecturally corresponding to approximations to the Weil– Petersson metric near large complex structure limit for the mirror. In particular, the naturally defined Riemannian metric (defined via cup-product) on a level set of the Kähler cone is se...

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3, and let Γ be a nonempty closed subset of M . The negative case of the Singular Yamabe Problem concerns the existence and behavior of a complete metric ĝ on M\Γ that has constant negative scalar curvature and is pointwise conformally related to the smooth metric g. Previous results have shown that when Γ is a smooth submanifold of d...

We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{otimes k}$ of a finite dimensional representation $V$ of a connected reductive group. We describe the cone generated by $S$ as the cone over the weight polytope of $V$ intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in $V^{otime...

We present an $LC$ circuit model that supports a tilted ``Dirac cone'' in its spectrum. The tilt of the Dirac cone is specified by parameters consisting mutual inductance between neighboring sites and capacitance ${C}_{0}$ at every lattice site. These can be completely measured impedance spectroscopy. Given described background spacetime metric, spectroscopy perfectly provide (local) informatio...