Knotted structures in high-energy Beltrami fields on the torus and the\n sphere

2015/05/07 by Alberto Enciso, Daniel Peralta‐Salas, Enciso, Alberto +3 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1505.01605

Abstract

Let S be a finite union of (pairwise disjoint but possibly knotted and\nlinked) closed curves and tubes in the round sphere S³ or in the flat torus\nT³. In the case of the torus, S is further assumed to be contained in a\ncontractible subset of T³. In this paper we show that for any sufficiently\nlarge odd integer \λ there exists a Beltrami field on S³ or T³\nsatisfying curl u = \λ u and with a collection of vortex lines and vortex\ntubes given by S, up to an ambient diffeomorphism.\n

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