Overtwisted energy-minimizing curl eigenfields

Abstract

We consider energy-minimizing divergence-free eigenfields of the curl operator in dimension three from the perspective of contact topology. We give a negative answer to a question of Etnyre and the first author by constructing curl eigenfields which minimize $L^2$ energy on their co-adjoint orbit, yet are orthogonal to an overtwisted contact structure. We conjecture that $K$-contact structures on $S^1$-bundles always define tight minimizers, and prove a partial result in this direction.

published version

References in corpus (3)

• Contact Topology and Hydrodynamics
• Adiabatic limits of Seiberg-Witten equations on Seifert manifolds
• On the contact geometry of nodal sets

Cited by in corpus (3)

• Contact structures and Beltrami fields on the torus and the sphere
• Tight Beltrami fields with symmetry
• Energy minimizing Beltrami fields on Sasakian 3-manifolds