Related papers: Global hypoellipticity and global solvability for …
We analyze the sharpness of the Sobolev order for left-invariant vector fields on compact Riemannian manifolds. Utilizing techniques from pseudo-differential operator theory and microlocal analysis, we investigate the asymptotic behavior of…
We introduce a class of divergence-free vector fields on $\mathbb{R}^3$ obtained after a suitable localization of Beltrami fields. First, we use them as initial data to construct unique global smooth solutions of the three dimensional…
Taking advantage of a previously developed method, which allows to map solutions of General Relativity into a broad family of theories of gravity based on the Ricci tensor (Ricci-based gravities), we find new exact analytical scalar field…
Effective field theory methods suggest that some rather-general extensions of General Relativity include, or are mimicked by, certain higher-order curvature corrections, with coupling constants expected to be small but otherwise arbitrary.…
For any compact oriented manifold $M$, we show that that the top degree multi-vector fields transverse to the zero section of $\wedge^{\text{top}}TM$ are classified, up to orientation preserving diffeomorphism, in terms of the topology of…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
We extend the results of generic vanishing theory to polarizable real Hodge modules on compact complex tori, and from there to arbitrary compact K\"ahler manifolds. As applications, we obtain a bimeromorphic characterization of compact…
We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \sigma $ is not constant on $ \Char P $.…
These notes present Sobolev-Gagliardo-Nirenberg endpoint estimates for classes of homogeneous vector differential operators. Away of the endpoint cases, the classical Calder\'on-Zygmund estimates show that the ellipticity is necessary and…
A classical result of D. McDuff asserts that a simply-connected complete Kaehler manifold $(M,g,\omega)$ with non positive sectional curvature admits global symplectic coordinates through a symplectomorphism $\Psi: M\rightarrow R^{2n}$…
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…
We study universal enveloping Hopf algebras of Lie algebras in the category of weakly complete vector spaces over the real and complex field.
In one complex variable, the existence of a compactly supported solution to the Cauchy-Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via…
This article presents an investigation of global properties of a class of differential operators on $\mathbb{T}^1\times\mathbb{R}$. Our approach involves the utilization of a mixed Fourier transform, incorporating both partial Fourier…
We extend the classical Fuller index, and use this to prove that for a certain general class of vector fields $X$ on a compact smooth manifold, if a homotopy of smooth non-singular vector fields starting at $X$ has no sky catastrophes as…
In this paper, we give an explicit description of holomorphic polyvector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties.
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that…
The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain…
The existence of a vector field on a compact Kaehler manifold with nonempty zero locus and the properties of this zero locus strongly influence the geometry of the manifold. For example, J. Wahl proved that the existence of a vector field…
We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…