#### Volume 11, issue 3 (2011)

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Dividing sets as nodal sets of an eigenfunction of the Laplacian

### Samuel T Lisi

Algebraic & Geometric Topology 11 (2011) 1435–1443
##### Abstract

We show that for any convex surface $S$ in a contact $3$–manifold, there exists a metric on $S$ and a neighbourhood contact isotopic to $S×I$ with the contact structure given by $ker\left(u\phantom{\rule{0.3em}{0ex}}dt-\star du\right)$ where $u$ is an eigenfunction of the Laplacian on $S$ and $\star$ is the Hodge star from the metric on $S$. This answers a question posed by Komendarczyk [Trans. Amer. Math. Soc. 358 (2006) 2399–2413].

##### Keywords
contact topology, convex surface, dividing set, nodal set, eigenfunction Laplacian
Primary: 57R17
Secondary: 53D10
##### Publication
Received: 1 April 2010
Revised: 3 November 2010
Accepted: 10 January 2011
Published: 17 May 2011
##### Authors
 Samuel T Lisi Département de Mathématique Université Libre de Bruxelles, CP 218 Boulevard du Triomphe B-1050 Bruxelles Belgium http://homepages.ulb.ac.be/~samulisi/