Dividing sets as nodal sets of an eigenfunction of the Laplacian

Details Dividing sets as nodal sets of an eigenfunction of the Laplacian Dividing sets as nodal sets of an eigenfunction of the Laplacian

2010-04-01

arxiv.org/abs/1004.0238v1

Mathematics

Symplectic Geometry

6 pages, 1 figure

Scientific paper

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 $S \times I$ with contact
structure given as $\ker(ud - \star du)$ 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.

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