Related papers: Symmetric cubic polynomials
Hyperbolic polynomials are monic real-rooted polynomials. By Bronshtein's theorem, the increasingly ordered roots of a hyperbolic polynomial of degree $d$ with $C^{d-1,1}$ coefficients are locally Lipschitz and the solution map…
The notion of relatedness loci in the parabolic slices Per_1(e^{2\pi i p/q}) in moduli space of quadratic rational maps is introduced. They are counterparts of the disconnectedness or escape locus in the slice of quadratic polynomials. A…
We develop dynamical theory for the family of holomorphic correspondences $\mathcal{F}_a$ proved by the current authors to be matings between the modular group and parabolic rational maps in the Milnor slice $Per_1(1)$ (in 'Mating quadratic…
A polynomial knot in $\mathbb{R}^n$ is a smooth embedding of $\mathbb{R}$ in $\mathbb{R}^n$ such that the component functions are real polynomials. In the earlier paper with Mishra, we have studied the space $\mathcal{P}$ of polynomial…
This is a sequel to the papers [OW1], [OW2]. In [OW1], the authors introduced a canonical affine connection on $M$ associated to the contact triad $(M,\lambda,J)$. In [OW2], they used the connection to establish a priori $W^{k,p}$-coercive…
Given graphs $X$ and $Y$, we define two conic feasibility programs which we show have a solution over the completely positive cone if and only if there exists a homomorphism from $X$ to $Y$. By varying the cone, we obtain similar…
We prove that the Laurent polynomial in $\mathbb{Z}[q^{\pm 1}]$ that is the top coefficient of the Links-Gould invariant of the boundary of a Seifert surface is multiplicative under plumbing of surfaces. We deduce that the Links-Gould…
We investigate the holonomy group of a linear metric connection with skew-symmetric torsion. In case of the euclidian space and a constant torsion form this group is always semisimple. It does not preserve any non-degenerated 2-form or any…
For the study of the 2-dimensional space of cubic polynomials, J. Milnor considers the complex 1-dimensional slice S_n of the cubic polynomials which have a super-attracting orbit of period n. He gives in [M4] a detailed conjectural picture…
We investigate the local deformation space of 3-dimensional cone-manifold structures of constant curvature $\kappa \in \{-1,0,1\}$ and cone-angles $\leq \pi$. Under this assumption on the cone-angles the singular locus will be a trivalent…
We study the regularity of the roots of multiparameter families of complex univariate monic polynomials $P(x)(z) = z^n + \sum_{j=1}^n (-1)^j a_j(x) z^{n-j}$ with fixed degree $n$ whose coefficients belong to a certain subring $\mathcal C$…
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In…
Let (M,g) be a compact Riemannian three-dimensional manifold with boundary. We prove the compactness of the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface.…
In this article we provide a combinatorial sufficient (and conjecturally, necessary) condition (called $\alpha$-symmetry) for the mating of two postcritically finite polynomials in $\mathcal{S}_1$ to be obstructed. To do this, we study the…
The isolation intervals of the real roots of the real symbolic monic cubic polynomial $p(x) = x^3 + a x^2 + b x + c\,\,$ are found in terms of simple functions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$, $\pm…
We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. The construction of such mappings comes from our construction of non-trivial compact…
This article investigates the computation of the eigenmodes of the Laplacian operator in multi-connected three-dimensional spherical spaces. General mathematical results and analytical solutions for lens and prism spaces are presented.…
We derive local and global monotonic quantities associated to $p$-harmonic functions on manifolds with nonnegative scalar curvature. As applications, we obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the…
In this paper, we study the local connectivity and Hausdorff dimension for the boundaries of the bounded hyperbolic components in the space $\mathcal P_d$ of polynomials of degree $d\geq 3$. It is shown that for any non disjoint-type…
A family of N-qubit entanglement monotones invariant under stochastic local operations and classical communication (SLOCC) is defined. This class of entanglement monotones includes the well-known examples of the concurrence, the…