Related papers: Bounds for the Euclidean minima of function fields

The new property of minimal surfaces is obtained in this article.

The aim of this paper is to study the product of $n$ linear forms over function fields. We calculate the maximum value of the minima of the forms with determinant one when $n$ is small. The value is equal to the natural bound given by…

We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation…

We present a boundary version of a theorem about solenoidal unit vector fields with minimum energy on a spherical domain of an odd dimensional Euclidean sphere.

This paper gives, in generic situations, a complete classification of ruled minimal surfaces in pseudo-Euclidean space with arbitrary index. In addition, we discuss the condition for ruled minimal surfaces to exist, and give a…

Every Euclidean domain $R$ has a minimal Euclidean function, $\phi_R$. A companion paper \cite{Graves} introduced a formula to compute $\phi_{\mathbb{Z}[i]}$. It is the first formula for a minimal Euclidean function for the ring of integers…

Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible measurable invariant line fields of a rational function on its…

We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.

A variational phase space is constructed for a system of fields on Euclidean space with periodic boundary conditions. An extended action functional is defined such that the Euler-Lagrange equations generate a symplectic flow on the…

We define a modular function which is a generalization of the elliptic modular lambda function. We show this function and the modular invariant function generate the modular function field with respect to the principal congruence subgroup.…

A certain real number, depending on two neighbouring sides of a quadrilateral and the diagonal meeting these two sides at their common point, is shown to be invariant under affinity. As an application we demonstrate a nice formula for the…

In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations

In this paper, we study the approximation of negative plurifinely plurisubharmonic function defined on a plurifinely domain by an increasing sequence of plurisubharmonic functions defined in Euclidean domains.

An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…

In this paper we consider a class of prescribing curvature type equations on half Euclidean balls. Under suitable assumptions on the scalar curvature function and boundary mean curvature function we prove a min-max type inequality and the…

Balls are shown to have the smallest optimal constant, among all admissible Euclidean domains, in Poincar\'e type boundary trace inequalities for functions of bounded variation with vanishing median or mean value.

We determine upper and lower bounds for the minimal number of balls of a given radius needed to cover the space of schlicht functions.

The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the…

We prove new explicit conditional bounds for the residue at $s=1$ of the Dedekind zeta-function associated to a number field. Our bounds are concrete and all constants are presented with explicit numerical values.

This paper addresses to the problem of finding the (minimum) Euclidean distance between two linear varieties. This problem is, usually, solved minimising a target function. We propose a novel approach: to use the Moore-Penrose generalised…