Related papers: Beltrami fields with nonconstant proportionality f…
We consider the existence of Beltrami fields with a nonconstant proportionality factor $f$ in an open subset $U$ of $\mathbf{R}^3$. By reformulating this problem as a constrained evolution equation on a surface, we find an explicit…
We prove that bounded Beltrami fields must be symmetric if a proportionality factor depends on 2 variables in the cylindrical coordinate and admits a regular level set diffeomorphic to a cylinder or a torus.
In this work we study Beltrami fields with non-constant proportionality factor on $\mathbb{R}^3$. More precisely, we analyze the existence of vector fields $X$ satisfying the equations $curl(X)=fX$ and $div(X)=0$ for a given $f\in…
We consider the equation rotB+aB=0 (1) in the plane with a being a real-valued function and show that it can be reduced to a Vekua equation of a special form. In the case when a depends on one Cartesian variable a complete system of exact…
For a generic value of the central charge, we prove the holomorphic factorization of partition functions for free superconformal fields which are defined on a compact Riemann surface without boundary. The partition functions are viewed as…
Beltrami fields occur as stationary solutions of the Euler equations of fluid flow and as force free magnetic fields in magnetohydrodynamics. In this paper we discuss the role of Beltrami fields when considered as operators acting on a…
We study the conformal type of surfaces spread over the sphere via random quasiconformal maps. Constructing a random Beltrami coefficient on the complex plane, we obtain a locally quasiconformal homeomorphism with prescribed dilatation that…
The paper is devoted to an algebraic analogue of a geometric approach to the classical notion of complex dilatation suggested in the paper arXiv:1701.06259 [math.CV] by the author. At the same time it provides an invariant version of this…
A Beltrami field is an eigenvector of the curl operator. Beltrami fields describe steady flows in fluid dynamics and force free magnetic fields in plasma turbulence. By application of the Lie-Darboux theorem of differential geoemtry, we…
Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal…
Boundary conformal field theory (BCFT) is the study of conformal field theory (CFT) on manifolds with a boundary. We can use conformal symmetry to constrain correlation functions of conformal invariant fields. We compute two-point and…
Using open books, we prove the existence of a non-vanishing steady solution to the Euler equations for some metric in every homotopy class of non-vanishing vector fields of any odd dimensional manifold. As a corollary, any such field can be…
We consider foliations of compact complex manifolds by analytic curves. We suppose that the line bundle tangent to the foliation is negative. We show that in a generic case there exists a finitely smooth homeomophism, holomorphic on the…
This talk gives a review on how complex geometry and a Lagrangian formulation of 2-d conformal field theory are deeply related. In particular, how the use of the Beltrami parametrization of complex structures on a compact Riemann surface…
Non-relativistic conformal field theory describes many-body physics at unitarity. The correlation functions of the system are fixed by the requirement of conformal invariance. In this article, we discuss the correlation functions of scalar…
A 3-dimensional vector field $B$ is said to be Beltrami vector field (force free-magnetic vector field in physics), if $B\times(\nabla\times B)=0$. Motivated by our investigations on projective an polynomial superflows, and as an important…
We construct a set of non-rational conformal field theories that consist of deformations of Toda field theory for sl(n). Besides conformal invariance, the theories still enjoy a remnant infinite-dimensional affine symmetry. The case n=3 is…
In this article it is shown that the study of harmonic diffeomorphisms, with nonvanishing Hopf differential, reduces to the study of the Beltrami equation of a certain type: the imaginary part of the logarithm of the Beltrami function…
We consider the bulk $\phi^3$ deformation of the free boundary conformal field theory in the $\epsilon$ expansion. We determine the leading corrections to the scaling dimensions of boundary fundamental operators and some boundary operator…
We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank $(N,N')$, and their possible anomalies. Both classical and ghost conformally invariant multiplets of the left or right…