2018/10/19 by Alberto Enciso, Enciso, Alberto, Daniel Peralta-Salas +4 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Combinatorics #Contractible space #Diffeomorphism #Differential Geometry (math.DG) #Eigenfunction #Eigenvalues and eigenvectors #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hypersurface #Integer (computer science) #Lambda #Laplace operator #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum mechanics #Spectral Theory (math.SP) #Torus #math.AP #math.DG #math.SP
paper · pdf · doi:10.48550/arxiv.1810.09277
published in arXiv (Cornell University) (Cornell University) · 14 pages. arXiv admin note: text overlap with arXiv:1712.10310, arXiv:1505.01605
arxiv created 2018/10/19 · openalex publication_date 2018/10/19 · arxiv updated 2018/10/23 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
Let \Σ be an oriented compact hypersurface in the round sphere\n mathbbSn or in the flat torus mathbbTn, n\≥ 3. In the case of\nthe torus, \Σ is further assumed to be contained in a contractible subset\nof mathbbTn. We show that for any sufficiently large enough odd integer\nN there exists an eigenfunctions \ψ of the Laplacian on mathbbSn or\n mathbbTn satisfying \Δ \ψ=-\λ \ψ (with \λ=N(N+n-1)\nor N2 on mathbbSn or mathbbTn, respectively), and with a\nconnected component of the nodal set of \ψ given by~\Σ, up to an\nambient diffeomorphism.\n