One can't hear orientability of surfaces
| Autor: | David L. Webb, Pierre Bérard |
|---|---|
| Přispěvatelé: | Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Isospectral surfaces General Mathematics Boundary (topology) Mathematical proof 01 natural sciences Spectrum (topology) Orientability Dirichlet distribution Mathematics - Spectral Theory symbols.namesake Spectrum 0103 physical sciences FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] MSC2010: 58J50 58J32 0101 mathematics Spectral Theory (math.SP) Mathematics 010102 general mathematics 58J50 58J32 Surface (topology) Isospectral Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] symbols 010307 mathematical physics Preprint Laplacian [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] |
| Zdroj: | Mathematische Zeitschrift Mathematische Zeitschrift, Springer, 2021, https://doi.org/10.1007/s00209-021-02758-y |
| ISSN: | 0025-5874 1432-1823 |
| DOI: | 10.1007/s00209-021-02758-y |
| Popis: | The main result of this paper is that one cannot hear orientability of a surface with boundary. More precisely, we construct two isospectral flat surfaces with boundary with the same Neumann spectrum, one orientable, the other non-orientable. For this purpose, we apply Sunada's and Buser's methods in the framework of orbifolds. Choosing a symmetric tile in our construction, and adapting a folklore argument of Fefferman, we also show that the surfaces have different Dirichlet spectra. These results were announced in the {\it C. R. Acad. Sci. Paris S\'er. I Math.}, volume 320 in 1995, but the full proofs so far have only circulated in preprint form. Comment: Minor changes. Accepted for publication in Mathematische Zeitschrift |
| Databáze: | OpenAIRE |
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