One can’t hear orientability of surfaces
2021
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 C. R. Acad. Sci. Paris Ser. I Math., volume 320 in 1995, but the full proofs so far have only circulated in preprint form.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
30
References
0
Citations
NaN
KQI