Laplace operators with eigenfunctions whose nodal set is a knot

Alberto Enciso; David Hartley; Daniel Peralta-Salas

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arXiv · 1505.06684

Laplace operators with eigenfunctions whose nodal set is a knot

Alberto Enciso·David Hartley·Daniel Peralta-Salas

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Abstract

We prove that, given any knot $γ$ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set $u^{-1}(0)$ has a connected component given by $γ$. Higher dimensional analogs of this result will also be considered.

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BibTeX RIS

Alberto Enciso, David Hartley, Daniel Peralta-Salas. 2015-05-25. Laplace operators with eigenfunctions whose nodal set is a knot. https://arxiv.org/abs/1505.06684

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