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(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].

Keywords
contact topology, convex surface, dividing set, nodal set, eigenfunction Laplacian
Mathematical Subject Classification 2000
Primary: 57R17
Secondary: 53D10
References
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/