Related papers: On Positivity in Sasaki Geometry

We show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the singular locus, or the hypersurface contains a linear…

The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…

Using $S^1$-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn-Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various…

Let $M$ be a cancellative and commutative (additive) monoid. The monoid $M$ is atomic if every non-invertible element can be written as a sum of irreducible elements, which are also called atoms. Also, $M$ satisfies the ascending chain…

We consider finite-dimensional real vector spaces $X$ ordered by a closed cone $X_+$ with non-empty interior and study eventual nonnegativity of matrix semigroups $(e^{tA})_{t \ge 0}$ with respect to this cone. Our first contribution is the…

We prove that for any smooth polarized complex $n$-dimensional manifold $(X, L_X)$ which admits an extremal K\"ahler metric in $c_1(L_X)$, and for any integer $k$ large enough (in terms of a bound depending on $(X, L_X)$), the…

We obtain new exact solutions in Einstein Gauss-Bonnet gravity of every odd dimension higher than three. These new spacetimes are stationary but non-static, coupled with the Maxwell field, and asymptotic AdS at least locally. In order to…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

For a 4th order 3-dimensional symmetric tensor with its some entries $1$ or $-1$, we show the analytic sufficient and necessary conditions of its positive definiteness. By applying these conclusions, several strict inequalities is bulit for…

We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in K\"ahler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied…

Let $(g,X)$ be a Sasaki-Ricci soliton on a Sasakian manifold $S$. We prove that if $(S,g)$ admits a local Sasakian immersion in a Sasakian space form $S(N,c)$ of constant $\phi$-sectional curvature $c$, then $S$ is $\eta$-Einstein and its…

I describe a general scheme which associates conjugacy classes of tori in the contactomorphism group to transverse almost complex structures on a compact contact manifold. Moreover, to tori of Reeb type whose Lie algebra contains a Reeb…

Given a smooth convex cone in the Euclidean $(n+1)$-space ($n\geq2$), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If…

Phase transitions can occur in one-dimensional classical statistical mechanics at non-zero temperature when the number of components N of the spin is infinite. We show how to solve such magnets in one dimension for any N, and how the phase…

Positive curvature and bosons Compact positive curvature Riemannian manifolds M with symmetry group G allow Conner-Kobayashi reductions M to N, where N is the fixed point set of the symmetry G. The set N is a union of smaller-dimensional…

The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. The proof of our…

In this paper we study the 3-dimensional $(\varepsilon) $-para Sasakian manifolds. We obtain an necessary and sufficient condition for an $(\varepsilon ) $-para Sasakian 3 -manifold to be an indefinite space form. We show that a…

Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…

We address the conjecture proposed by Gabor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case, however, there exists a four-dimensional counterexample of a cone that is…

This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…