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Overtwisted energy-minimizing curl eigenfields

R. Ghrist·R. Komendarczyk
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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.

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R. Ghrist, R. Komendarczyk. 2015-09-11. Overtwisted energy-minimizing curl eigenfields. https://doi.org/10.1088/0951-7715%2F19%2F1%2F003

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