Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415007 | Journal of Functional Analysis | 2016 | 19 Pages |
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 uâ1(0) has a connected component given by γ. Higher dimensional analogs of this result will also be considered.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Alberto Enciso, David Hartley, Daniel Peralta-Salas,