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2011 Dividing sets as nodal sets of an eigenfunction of the Laplacian
Samuel T Lisi
Algebr. Geom. Topol. 11(3): 1435-1443 (2011). DOI: 10.2140/agt.2011.11.1435


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(udtdu) 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].


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Samuel T Lisi. "Dividing sets as nodal sets of an eigenfunction of the Laplacian." Algebr. Geom. Topol. 11 (3) 1435 - 1443, 2011.


Received: 1 April 2010; Revised: 3 November 2010; Accepted: 10 January 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1228.57010
MathSciNet: MR2821429
Digital Object Identifier: 10.2140/agt.2011.11.1435

Primary: 57R17
Secondary: 53D10

Keywords: contact topology , convex surface , dividing set , eigenfunction Laplacian , nodal set

Rights: Copyright © 2011 Mathematical Sciences Publishers

Vol.11 • No. 3 • 2011
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