Related papers: Quasi-continuous vector fields on RCD spaces

We show that certain field theory models, although non-integrable according to the usual definition of integrability, share some of the features of integrable theories for certain configurations. Here we discuss our attempt to define a…

We present a new, alternative interpretation of the vector-tensor multiplet as a 2-form in central charge superspace. This approach provides a geometric description of the (non-trivial) central charge transformations ab initio and is…

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector…

There is a chance that singleton fields, that in the context of strings and membranes have been regarded as topological gauge fields that can interact only at the boundary of anti-De Sitter space, at spatial infinity, may have a more…

We consider the problem of minimal volume vector fields on a given Riemann surface, specialising on the case of $M^\star$, that is, the arbitrary radius 2-sphere with two antipodal points removed. We discuss the homology theory of the unit…

Faddeev formulation of general relativity (GR) is considered where the metric is composed of ten vector fields or a ten-dimensional tetrad. Upon partial use of the field equations, this theory results in the usual GR. Earlier we have…

In this article, we introduce $\omega$-Bach tensor corresponding to one form $\omega$ and correspondingly introduce almost $\omega$-Bach solitons, thereby generalizing the existing notion of Bach tensor and almost Bach solitons. We…

We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.

This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential constraint, to closed $\mathcal{A}$-$p$ quasiconvexity of the…

We discuss various old and new definitions of the notion of a vector field on a convenient manifold that can be proved to give rise to Lie algebras, and are in finite dimensions equivalent to the standard notion of a vector field.

A local classification of semisimple algebras of vector fields on $\mathbb{C}^{3}$ is given, using the canonical forms of the Heisenberg algebra and of $sl(2,\mathbb{C})\times sl(2,\mathbb{C})$.

We develop a theory of measures, differential forms and Fourier tramsforms on some infinite-dimensional real vector spaces by generalizing the following two constructions: (a) The construction of the semiinfinite wedge power of a Tate…

We discuss a method for the construction of almost periodic solutions of the one dimensional analytic NLS with only Sobolev regularity both in time and space. This is the first result of this kind for PDEs.

We consider almost Einstein solitons $(V,\lambda)$ in a Riemannian manifold when $V$ is a gradient, a solenoidal or a concircular vector field. We explicitly express the function $\lambda$ by means of the gradient vector field $V$ and…

We revise the notion of the quasi-sectorial contractions. Our main theorem establishes a relation between semigroups of quasi-sectorial contractions and a class of m-sectorial generators. We discuss a relevance of this kind of contractions…

We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis…

This paper introduces a new object called the momentum tensor. Together with the velocity tensor it forms a basis for establishing the tensorial picture of classical and relativistic mechanics. Some properties of the momentum tensor are…

The compact set of homogeneous quadratic polynomials in $n$ real variables with modulus bounded by 1 on the unit sphere $S^{n-1}$ is trivially semi-definite representable. The compact set of homogeneous ternary quartics with modulus bounded…

We describe classes of toric varieties of codimension 2 which are either minimally defined by 3 binomial equations over any algebraically closed field, or are set-theoretic complete intersections in exactly one positive characteristic.

We propose a consistent approach to the definition of electric, magnetic, and toroidal multipole moments. Electric and magnetic fields are split into potential, vortex, and radiative terms, with the latter ones dropped off in the…