10 citations · 24 across the 10 of their papers we have counts for
10 papers
Charged particle motion in a strong magnetic field: Applications to plasma confinement
Ugo Boscain, Wadim Gerner
We derive the zero order approximation of a charged particle under the influence of a strong magnetic field in a mathematically rigorous manner and clarify in which sense this appr…
Optimal metrics for the first curl eigenvalue on 3-manifolds
Alberto Enciso, Wadim Gerner, Daniel Peralta-Salas
In this article we analyze the spectral properties of the curl operator on closed Riemannian 3-manifolds. Specifically, we study metrics that are optimal in the sense that they min…
Existence of optimal domains for the helicity maximisation problem among domains satisfying a uniform ball condition
Wadim Gerner
In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of -regular domains satisf…
A unique continuation theorem for exterior differential forms on Riemannian manifolds with boundary
Wadim Gerner
Aronszajn, Krzywicki and Szarski proved in \cite{AKS62} a strong unique continuation result for differential forms, satisfying a certain first order differential inequality, on Rie…
Isoperimetric problem for the first curl eigenvalue
Wadim Gerner
We consider an isoperimetric problem involving the smallest positive and largest negative curl eigenvalues on abstract ambient manifolds, with a focus on the standard model spaces.…
Optimal convex domains for the first curl eigenvalue
Alberto Enciso, Wadim Gerner, Daniel Peralta-Salas
We prove that there exists a bounded convex domain of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains…
Existence and structure of symmetric Beltrami flows on compact -manifolds
Wadim Gerner
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,…
Typical field lines of Beltrami flows and boundary field line behaviour of Beltrami flows on simply connected, compact, smooth manifolds with boundary
Wadim Gerner
We characterise the boundary field line behaviour of Beltrami flows on compact, connected manifolds with vanishing first de Rham cohomology group. Namely we show that except for an…
Zero set structure of real analytic Beltrami fields
Wadim Gerner
In this paper we prove a classification theorem for the zero sets of real analytic Beltrami fields. Namely, we show that the zero set of a real analytic Beltrami field on a real an…
Existence and characterisation of magnetic energy minimisers on oriented, compact Riemannian 3-manifolds with boundary in arbitrary helicity classes
Wadim Gerner
In this paper we deal with the existence, regularity and Beltrami field property of magnetic energy minimisers under a helicity constraint. We in particular tackle the problem of c…