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Laplace operators with eigenfunctions whose nodal set is a knot

Journal Article


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.

Authors


  •   Enciso, Alberto (external author)
  •   Hartley, David James.
  •   Peralta-Salas, Daniel (external author)

Publication Date


  • 2016

Geographic Focus


Citation


  • Enciso, A., Hartley, D. James. & Peralta-Salas, D. (2016). Laplace operators with eigenfunctions whose nodal set is a knot. Journal of Functional Analysis, 271 (1), 182-200.

Scopus Eid


  • 2-s2.0-84963956142

Ro Metadata Url


  • http://ro.uow.edu.au/asdpapers/708

Number Of Pages


  • 18

Start Page


  • 182

End Page


  • 200

Volume


  • 271

Issue


  • 1

Place Of Publication


  • United States

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.

Authors


  •   Enciso, Alberto (external author)
  •   Hartley, David James.
  •   Peralta-Salas, Daniel (external author)

Publication Date


  • 2016

Geographic Focus


Citation


  • Enciso, A., Hartley, D. James. & Peralta-Salas, D. (2016). Laplace operators with eigenfunctions whose nodal set is a knot. Journal of Functional Analysis, 271 (1), 182-200.

Scopus Eid


  • 2-s2.0-84963956142

Ro Metadata Url


  • http://ro.uow.edu.au/asdpapers/708

Number Of Pages


  • 18

Start Page


  • 182

End Page


  • 200

Volume


  • 271

Issue


  • 1

Place Of Publication


  • United States