99-168 S. Fournais
The Nodal Surface Of The Second Eigenfunction Of The Laplacian In ${\mathbf R}^D$ Can Be Closed (198K, PostScript) May 12, 99
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Abstract. We construct a set in ${\mathbf R}^D$ with the property that the nodal surface of the second eigenfunction of the Dirichlet Laplacian is closed, i.e. does not touch the boundary of the domain. The construction is explicit in all dimensions $D \geq 2$ and we obtain explicit control of the connectivity of the domain.

Files: 99-168.src( 99-168.keywords , nodal.ps )