Geodesic
Dividing sets as nodal sets of an eigenfunction of the Laplacian
Lisi, Samuel T1
1Département de Mathématique, Université Libre de Bruxelles, CP 218, Boulevard du Triomphe, B-1050 Bruxelles, Belgium
Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1435-1443
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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(udt − ⋆du) where u is an eigenfunction of the Laplacian on S and ⋆ is the Hodge star from the metric on S. This answers a question posed by Komendarczyk [Trans. Amer. Math. Soc. 358 (2006) 2399–2413].

DOI : 10.2140/agt.2011.11.1435
Keywords: contact topology, convex surface, dividing set, nodal set, eigenfunction Laplacian

Lisi, Samuel T  1

1 Département de Mathématique, Université Libre de Bruxelles, CP 218, Boulevard du Triomphe, B-1050 Bruxelles, Belgium 
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Lisi, Samuel T. Dividing sets as nodal sets of an eigenfunction of the Laplacian. Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1435-1443. doi: 10.2140/agt.2011.11.1435

[1] J Etnyre, R Komendarczyk, P Massot, Contact metric manifolds and tight contact structures

[2] E Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991) 637

[3] R Komendarczyk, On the contact geometry of nodal sets, Trans. Amer. Math. Soc. 358 (2006) 2399

[4] R Komendarczyk, Nodal sets and contact structures, PhD thesis, Georgia Institute of Technology (2008)

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