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Nodal Sets and Contact Structures
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In this work, the author studies contact structures§via adapted Riemannian metrics. The main observation§is a relation between characteristic surfaces of§contact structures and zero sets of solutions to§certain subelliptic partial differential equations.§This relation makes it possible to derive, under a§symmetry assumption, lower bounds for the volume of§the manifold supporting overtwisted or virtually§overtwisted contact structures arising from a certain§class of invariant curl eigenfields. Further, it has§implications in the energy relaxation of this special§class of fluid flows. Specifically, the author§provides a counterexample to the conjecture of Etnyre§and Ghrist posed in their work on hydrodynamics of§contact structures.
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