Related papers: Beltrami fields with a nonconstant proportionality…
We show that for almost every given symmetry transformation of a Riemannian manifold there exists an eigenvector field of the curl operator, corresponding to a non-zero eigenvalue, which obeys the symmetry. More precisely, given a smooth,…
The question of whether a closed, orientable manifold can admit a nontrivial vector field that is parallel with respect to some Riemannian metric is a classical problem in Differential Geometry, first posed by S. S. Chern [11]. In this…
A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf…
Central quantities in spectroscopy and magnetism of transition ions in crystals are crystal field parameters (CFPs). Nature self-imposed limits on orthorhombic and lower symmetry CFPs, and existence of intrinsically incomparable CFP sets…
Helical symmetry is invariance under a one-dimensional group of rigid motions generated by a simultaneous rotation around a fixed axis and translation along the same axis. The key parameter in helical symmetry is the step or pitch, the…
We estimate the Hoelder exponent $\alpha$ of solutions to the Beltrami equation $\dbar f=\mu\de f$, where the Beltrami coefficient satisfies $\|\mu\|_\infty<1$. Our estimate improves the classical estimate $\alpha\ge\|K_\mu\|^{-1}$, where…
For any dimension $d\geq 3$ we construct $C^{1}$-open subsets of the space of $C^{3}$ vector fields such that the flow associated to each vector field is Axiom A and exhibits a non-trivial attractor which mixes exponentially with respect to…
In this paper we compute higher particle form factors of branch point twist fields. These fields were first described in the context of massive 1+1-dimensional integrable quantum field theories and their correlation functions are related to…
New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\bar{\partial} f = \mu \partial f + \nu \overline{\partial f}$ for discontinuous Beltrami coefficients $\mu$ and $\nu$ are obtained,…
We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…
Differential calculus on the space of asymptotically linear curves is developed. The calculus is applied to the vortex filament equation in its Hamiltonian description. The recursion operator generating the infinite sequence of commuting…
For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…
We consider the spatially inhomogeneous Boltzmann equation for inelastic hard-spheres, with constant restitution coefficient $\alpha\in(0,1)$, under the thermalization induced by a host medium with a fixed Maxwellian distribution and any…
We prove a generalization of the Conley conjecture: Every Hamiltonian diffeomorphism of a closed symplectic manifold has infinitely many periodic orbits if the first Chern class vanishes over the second fundamental group. In particular, we…
We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of…
In this paper we study the parabolic evolution equation $\partial_t u=(|Du|^{2}+2|\det Du|)^{-1} \Delta u$, where $u : M\times[0,\infty) \to N$ is an evolving map between compact flat surfaces. We use a tensor maximum principle for the…
We study Beltrami-type equations with two given complex characteristics. Under certain conditions on the complex coefficients, we obtained theorems on the existence of homeomorphic $ ACL $ -solutions of this equation. In addition, for some…
Let $q$ be a quadratic form over a field $F$ and let $L$ be a field extension of $F$ of odd degree. It is a classical result that if $q_L$ is isotropic (resp. hyperbolic) then $q$ is isotropic (resp. hyperbolic). In turn, given two…
We study a family of fermionic extensions of the Camassa-Holm equation. Within this family we identify three interesting classes: (a) equations, which are inherently hamiltonian, describing geodesic flow with respect to an H^1 metric on the…
Invariance properties of physical systems govern their behavior: energy conservation in turbulence drives a wide distribution of energy among modes, observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of…