Related papers: Polynomials on Parabolic Manifolds

We establish necessary and sufficient conditions for determining when a flat manifold can occur as a cusp cross-section within a given commensurability class of cusped arithmetic hyperbolic manifolds. This reduces the problem of identifying…

In the space of cubic polynomials, Milnor defined a notable curve $\mathcal S_p$, consisting of cubic polynomials with a periodic critical point, whose period is exactly $p$. In this paper, we show that for any integer $p\geq 1$, any…

Very recently, the Fridman function of a complex manifold $X$ has been identified as a dual of the squeezing function of $X$. In this paper, we prove that the Fridman function for certain hyperbolic complex manifold $X$ is bounded above by…

We prove a polynomial upper bound on the number of resonances in a disc whose radius tends to infinity for even asymptotically hyperbolic manifolds with real-analytic ends. Our analysis also gives a similar upper bound on the number of…

A polynomial is called self-reciprocal (or palindromic) if the sequence of its coefficients is palindromic. In this paper we enumerate self-reciprocal irreducible monic polynomials over a finite field with prescribed leading coefficients.…

We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…

Suppose $(M,g)$ is a Riemannian manifold having dimension $n$, nonnegative Ricci curvature, maximal volume growth and unique tangent cone at infinity. In this case, the tangent cone at infinity $C(X)$ is an Euclidean cone over the…

Regarding polynomial functions on a subset $S$ of a non-commutative ring $R$, that is, functions induced by polynomials in $R[x]$ (whose variable commutes with the coefficients), we show connections between, on one hand, sets $S$ such that…

Periodic geodesics on the modular surface correspond to periodic orbits of the geodesic flow in its unit tangent bundle $\mathrm{PSL}_2(\mathbb{Z})\backslash\mathrm{PSL}_2(\mathbb{R})$. The complement of any finite number of orbits is a…

We define eventually symmetric functions to be those power series of bounded degree in infinitely many variables that are invariant under interchanging all the variables with large enough indices. We show how this ring $\tilde{\Lambda}$ is…

Given a complete isometric immersion $\phi: P^m \longrightarrow N^n$ in an ambient Riemannian manifold $N^n$ with a pole and with radial sectional curvatures bounded from above by the corresponding radial sectional curvatures of a radially…

Motivated by the finiteness of the set of automorphisms Aut(X) of a projective manifold X, and by Kobayashi-Ochiai's conjecture that a projective manifold dim(X)-analytically hyperbolic (also known as strongly measure hyperbolic) should be…

Sylvester equations $AX-XB=C$ have unique solutions for all $C$ when the spectra of $A$ and $B$ are disjoint. Here $A$ and $B$ are bounded operators in Banach spaces. We discuss the existence of polynomials $p$ such that the spectra of…

``What kind of ring can be represented as the singular cohomology ring of a space?'' is a classic problem in algebraic topology, posed by Steenrod. In this paper, we consider this problem when rings are the graded Stanley-Reisner rings, in…

The first essential ingredient to build up Stein's method for a continuous target distribution is to identify a so-called \textit{Stein operator}, namely a linear differential operator with polynomial coefficients. In this paper, we…

In this note, we consider the linear topological invariant {\Omega}-tilda for Fr\'echet spaces of global analytic functions on Stein manifolds. We show that O(M), for a Stein manifold M, enjoys the property {\Omega}-tilda if and only if…

Suppose that $(X, g)$ is a conformally compact $(n+1)$-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set $K \subset X$ the sectional curvatures of $g$ are identically equal to minus one. We prove…

In this article, we study compactifications of homogeneous spaces coming from equivariant, open embeddings into a generalized flag manifold $G/P$. The key to this approach is that in each case $G/P$ is the homogeneous model for a parabolic…

In this series of articles, we analyse the level-sets of length functions on the moduli space of compact hyperbolic surfaces of fixed genus. This work ultimately culminates in a proof that typical hyperbolic surfaces have an optimal…

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…