Related papers: Energy and volume of vector fields on spherical do…
We give a new proof of the well-known result that the minimal volume vector fields on $\mathbb{S}^3(r)$ are the Hopf vector fields. Such proof relies again on calibration theory, arising here from a systematic point of view given by a…
In this short note, we employ well-known results to improve the lower bound for the constant associated with the linear term in the asymptotic expansion of the minimal logarithmic energy on the sphere.
In these short notes we characterize the loxodromic unit vector fields on antipodally punctured Euclidean spheres as the only ones achieving a lower bound for the volume functional depending on the Poincar\'e indexes around their…
Local supersymmetry leads to boundary conditions for fermionic fields in one-loop quantum cosmology involving the Euclidean normal to the boundary and a pair of independent spinor fields. This paper studies the corresponding classical…
Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…
The role of the domain geometry for the statistical mechanics of 2D Euler flows is investigated. It is shown that for a spherical domain, there exists invariant subspaces in phase space which yield additional angular momentum, energy and…
We study the boundary limits of the Carath\'eodory and Kobayashi-Eisenman volume elements on smoothly bounded convex finite type domains and also on Levi corank one domains.
In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of…
The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron, which is in a 3-dimensional spherical space of constant curvature +1. One formula is given in terms of dihedral angles, and another one is…
We study vector minimizers u of the Allen-Cahn functional with potentials possessing N global minima defined on bounded domains, with certain geometrical features and Dirichlet conditions on the boundary. We derive a sharp lower bound for…
We analyze the effect of a finite volume on the thermodynamic potentials of a relativistic quantum field theory defined on a hypertorus at vanishing chemical potential. Using the symmetries of the Euclidean partition function, we interpret…
In this paper, we define Euclidean minima for function fields and give some bound for this invariant. We furthermore show that the results are analogous to those obtained in the number field case.
We show that the volume of any Riemannian metric on a three sphere is bounded below by the length of the shortest closed curve that links its antipodal image. In particular, the volume is bounded below by the minimum of the length of the…
Euclidean field theory on 4-dimensional sphere is suggested for the study of high energy multiparticle production. The singular classical field configurations are found in scalar and SU(2)-gauge theories and the cross section of 2->n…
Let $C_{\theta}$ be a circular cone in Euclidean space $\mathbb{R}^{3}$,which apex is the origin and apex angle of the cone is $\theta\in \left(\pi/3, \pi\right)$. Let $M_\theta$ be the class of compact convex domains in Euclidean space…
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…
This paper is concerned with a structural analysis of euclidean field theories on the euclidean sphere. In the first section we give proposal for axioms for a euclidean field theory on a sphere in terms of C*-algebras. Then, in the second…
We consider the problem of estimating the volume of a compact domain in a Euclidean space based on a uniform sample from the domain. We assume the domain has a boundary with positive reach. We propose a data splitting approach to correct…
A detailed analysis of the phase trajectories of cosmological models based on classical and scalar fields near surfaces of zero effective energy has been carried out. A study of the differential parameters of the convergence of phase…
We prove, under suitable conditions, a lower bound on the number of pinned distances determined by small subsets of two-dimensional vector spaces over fields. For finite subsets of the Euclidean plane we prove an upper bound for their…