We show that for any convex surface in a contact –manifold, there exists a metric on and a neighbourhood contact isotopic to with the contact structure given by where is an eigenfunction of the Laplacian on and is the Hodge star from the metric on . This answers a question posed by Komendarczyk [Trans. Amer. Math. Soc. 358 (2006) 2399–2413].
Samuel T Lisi. "Dividing sets as nodal sets of an eigenfunction of the Laplacian." Algebr. Geom. Topol. 11 (3) 1435 - 1443, 2011. https://doi.org/10.2140/agt.2011.11.1435