Abstract In this paper, we prove a classification theorem for the zero sets of real analytic Beltrami fields. Namely, show that set field on analytic, connected 3-manifold without boundary is either empty after removing its isolated points or can be written as countable, locally finite union differentiably embedded, 1-dimensional submanifolds with (possibly empty) and tame knots. Further, consi...

Following Bojarski and Vekua, we have studied the Dirichlet problem $$ \underset{z\to \zeta }{\lim}\operatorname{Re}\ f(z)=\varphi \left(\zeta \right) as z ? ?, ? D, ? ?D, with continuous boundary data ?(?) in bounded domains D of complex plane ?, where f satisfies degenerate Beltrami equation {f}_{\overline{z}}=\mu (z){f}_z,\left|\mu (z)\right|<1 , a.e. D. Assuming that is an arbitrary simply ...

Motivated by Poincar\'e's orbits going to infinity in the (restricted) three-body (see [26] and [6]), we investigate generic existence of heteroclinic-like a neighbourhood critical set $b$-contact form. This is done using singular counterpart [3] Etnyre--Ghrist's contact/Beltrami correspondence [9], genericity results concerning eigenfunctions Laplacian established Uhlenbeck [29]. Specifically,...

We study harmonic maps between surfaces, that are solutions to a nonlinear elliptic PDE. In Refs. Minsky (1992); Wolf (1989) it was proved diffeomorphisms, with nonvanishing Hopf differential, satisfy Beltrami equation of certain type: the imaginary part logarithm coefficient coincides differential. Therefore, is function. The real satisfies an differential equation, which in case constant curv...