Zobrazeno 1 - 10
of 35
pro vyhledávání: '"Gerner, Wadim"'
Autor:
Gerner, Wadim
In [J. Cantarella, J. Parsley, J. Geom. Phys. 60:1127 (2010)] Cantarella and Parsley introduced the notion of submanifold helicity. In the present paper we investigate properties of surface helicity and in particular answer two open questions posed i
Externí odkaz:
http://arxiv.org/abs/2408.00492
Autor:
Gerner, Wadim
We investigate properties of the image and kernel of the Biot-Savart operator in the context of stellarator designs for plasma fusion. We first show that for any given coil winding surface (CWS) the image of the Biot-Savart operator is $L^2$-dense in
Externí odkaz:
http://arxiv.org/abs/2311.03108
Autor:
Gerner, Wadim
In the present work we present a general framework which guarantees the existence of optimal domains for isoperimetric problems within the class of $C^{1,1}$-regular domains satisfying a uniform ball condition as long as the desired objective functio
Externí odkaz:
http://arxiv.org/abs/2305.13642
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 minimize the first curl eigenvalue among any other metric of the same vol
Externí odkaz:
http://arxiv.org/abs/2305.06681
Autor:
Gerner, Wadim
Aronszajn, Krzywicki and Szarski proved in \cite{AKS62} a strong unique continuation result for differential forms, satisfying a certain first order differential inequality, on Riemannian manifolds with empty boundary. The present paper extends this
Externí odkaz:
http://arxiv.org/abs/2207.02029
Autor:
Gerner, Wadim
Publikováno v:
Journal of Mathematical Analysis and Applications, 519 (2023), 126808
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. We in particular show that the corresponding eigenvalues on optimal d
Externí odkaz:
http://arxiv.org/abs/2203.00718
We prove that there exists a bounded convex domain $\Omega \subset \mathbf{R}^3$ of fixed volume that minimizes the first positive curl eigenvalue among all other bounded convex domains of the same volume. We show that this optimal domain cannot be a
Externí odkaz:
http://arxiv.org/abs/2202.09204
Autor:
Gerner, Wadim
Publikováno v:
Differential Geometry and its Applications, 78 (2021), 101801
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, compact, or
Externí odkaz:
http://arxiv.org/abs/2006.14507
Autor:
Gerner, Wadim
Publikováno v:
J. Geom. Anal. 31 (2021), 9928-9950
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 analytic, connected $3$-manifold without boundary is either empty after
Externí odkaz:
http://arxiv.org/abs/2005.07620
Autor:
Gerner, Wadim
Publikováno v:
Ann. Global Anal. Geom. 60 (2021), 65-82
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 at most nowhere dense subset of the boundary, on which the Beltrami f
Externí odkaz:
http://arxiv.org/abs/2005.06590