Universitat de Barcelona
2023-03-17T08:32:03Z
2023-03-17T08:32:03Z
2021-02-25
2023-03-17T08:32:03Z
Despite the moduli space of triangles being three dimensional, we prove the existence of two triangles which are not isometric to each other for which the first, second and fourth Dirichlet eigenvalues coincide, establishing a numerical observation from Antunes-Freitas [1]. The two triangles are far from any known, explicit cases. To do so, we develop new tools to rigorously enclose eigenvalues to a very high precision, as well as their position in the spectrum. This result is also mentioned as (the negative) part of [35, Conjecture 6.46], [23, Open Problem 1] and [39, Conjecture 3].
Article
Accepted version
English
Varietats (Matemàtica); Anàlisi global (Matemàtica); Teoria espectral (Matemàtica); Manifolds (Mathematics); Global analysis (Mathematics); Spectral theory (Mathematics)
Elsevier
Versió postprint del document publicat a: https://doi.org/10.1016/j.jde.2020.11.002
Journal of Differential Equations, 2021, vol. 275, p. 920-938
https://doi.org/10.1016/j.jde.2020.11.002
cc-by-nc-nd (c) Elsevier, 2021
https://creativecommons.org/licenses/by-nc-nd/4.0/
