2022-07-062022-07-062021-04-17Enciso, A., Peralta Salas, D. y Torres de Lizaur, F.J. (2021). High-Energy Eigenfunctions of the Laplacian on the Torus and the Sphere with Nodal Sets of Complicated Topology. En Springer Proceedings in Mathematics & Statistics (245-261), Sendai, Japan: Springer.2194-10092194-1017https://hdl.handle.net/11441/135039Let Σ be an oriented compact hypersurface in the round sphere Sn or in the flat torus Tn, n≥3. In the case of the torus, Σ is further assumed to be contained in a contractible subset of Tn. We show that for any sufficiently large enough odd integer N there exists an eigenfunctions ψ of the Laplacian on Sn or Tn satisfying Δψ=−λψ (with λ=N(N+n−1) or N2 on Sn or Tn, respectively), and with a connected component of the nodal set of ψ given by Σ, up to an ambient diffeomorphism.application/pdf14 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Eigenfunctions of the LaplacianNodal setsIsotopy typeInverse localizationinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess10.1007/978-981-33-4822-6_7