Related papers: Weak and Strong Extremal Biquadratics

An $n\times n$ real matrix $Q$ is quasi-orthogonal if $Q^{\top}Q=qI_{n}$ for some positive real number $q$. If $M$ is a principal sub-matrix of a quasi-orthogonal matrix $Q$, we say that $Q$ is a quasi-orthogonal extension of $M$. In a…

For the ternary quadratic form Q(x) = x^2 + y^2 - z^2 and a non-zero Pythagorean triple x_0 in Z^3 lying on the cone Q(x) = 0, we consider an orbit O = x_0 Gamma of a finitely generated subgroup Gamma < SO_Q(Z) with critical exponent…

We consider real forms of relatively minimal rational surfaces F_m. Connected components of moduli of real non-singular curves in |-2K_{F_m}| had been classified recently for m=0, 1, 4 in math.AG/0312396. Applying similar methods, here we…

In this paper we study unitary Ramond twisted representations of minimal $W$-algebras. We classify all such irreducible highest weight representations with a non-Ramond extremal highest weight (unitarity in the Ramond extremal case, as well…

We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (1993) and is in contrast to the fact that any metric space embeds coarsely into an Alexandrov space…

In this paper, we study the quasisymmetric embeddability of weak tangents of metric spaces. We first show that quasisymmetric embeddability is hereditary, i.e., if $X$ can be quasisymmetrically embedded into $Y$, then every weak tangent of…

We develop the theory of almost-holomorphic and quasimodular forms for orthogonal groups of a lattice of signature $(2,n)$ through orthogonal lowering and raising operators. The interactions with the regularized theta lift of Borcherds is a…

Let (X,\Omega) be a closed polarized complex manifold, g be an extremal metric on X that represents the K\"ahler class \Omega, and G be a compact connected subgroup of the isometry group Isom(X,g). Assume that the Futaki invariant relative…

An almost Fuchsian manifold is a hyperbolic 3-manifold of the type $S\times \mathbb{R}$ which admits a closed minimal surface (homeomorphic to $S$) with the maximum principal curvature $\lambda_0 <1$, while a weakly almost Fuchsian manifold…

We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary $1$-strata. As a consequence, by using a general criterion for…

We study the weak universality of the two-dimensional fractional nonlinear wave equation. For a sequence of Hamiltonians of high-degree potentials scaling to the fractional $\Phi_2^4$, we first establish a \emph{sufficient and almost…

Let $V$ be a symmetric convex body in $\R^m$. We prove sharp Bernstein-type inequalities for entire functions of exponential type with the spectrum in $V$ and discuss certain properties of the extremal functions. Markov-type inequalities…

In this short article, we establish a rigidity theorem for pairs of hyperquadrics in a weaker sense, i.e., we impose a condition that minimal rational curves are preserved, which is stronger than inheriting a sub-VMRT structure, a notion…

The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…

Many important problems in extremal combinatorics can be be stated as proving a pure binomial inequality in graph homomorphism numbers, i.e., proving that…

Looking at bivariate copulas from the perspective of conditional distributions and considering weak convergence of almost all conditional distributions yields the notion of weak conditional convergence. At first glance, this notion of…

This paper is concerned with the construction of extremal elliptic K3 surfaces. It gives a complete treatment of those fibrations which can be derived from rational elliptic surfaces by easy manipulations of their Weierstrass equations. In…

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler-Bardeen theorem the anomalous longitudinal part of the…

It is a conjecture of Koll\'ar that a variety $X$ with rational singularities in some open subvariety $U$ has a rationalification; that is, a proper, birational morphism $f: Y \rightarrow X$ such that $Y$ has rational singularities, and…

We study totally positive definite quadratic forms over the ring of integers $\mathcal{O}_K$ of a totally real biquadratic field $K=\mathbb{Q}(\sqrt{m}, \sqrt{s})$. We restrict our attention to classical forms (i.e., those with all…