Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip
| Autor: | Pierre Bérard, Bernard Helffer, Rola Kiwan |
|---|---|
| Přispěvatelé: | Institut Fourier (IF), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques Jean Leray (LMJL), Université de Nantes - Faculté des Sciences et des Techniques, Université de Nantes (UN)-Université de Nantes (UN)-Centre National de la Recherche Scientifique (CNRS), American University in Dubai, Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN) |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Spectral theory General Mathematics MSC (2010): 58C40 49Q10 Möbius strip 01 natural sciences Square (algebra) Mathematics - Spectral Theory symbols.namesake Nodal sets Dirichlet eigenvalue [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Euler characteristic 0103 physical sciences [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematical Physics Eigenvalues and eigenvectors Mathematics Courant theorem 010102 general mathematics 2010: 58C40 49Q10 Mathematics::Spectral Theory Eigenfunction 16. Peace & justice Surface (topology) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] symbols 010307 mathematical physics Laplacian [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] |
| Zdroj: | Portugaliae Mathematica Portugaliae Mathematica, European Mathematical Society Publishing House, 2021, 78 (1), pp.1--41 |
| ISSN: | 0032-5155 1662-2758 |
| DOI: | 10.4171/pm/2059 |
| Popis: | The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, \ldots . A natural toy model for further investigations is the M\"obius strip, a non-orientable surface with Euler characteristic $0$, and particularly the "square" M\"obius strip whose eigenvalues have higher multiplicities. In this case, we prove that the only Courant-sharp Dirichlet eigenvalues are the first and the second, and we exhibit peculiar nodal patterns. Comment: Revised version prior to publication. Accepted for publication in Portugaliae Mathematica |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|