Spectral theory of translation surfaces : A short introduction
Séminaire de théorie spectrale et géométrie, Volume 28  (2009-2010), p. 51-62

We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum

On définit les surfaces de translation et le Laplacien associé à la métrique euclidienne (avec singularités). Ce laplacien n’est pas essentiellement auto-adjoint et on rappelle la façon dont les extensions auto-adjointes sont caractérisées. Il y a deux choix naturels dont on montre que les spectres coïncident.

DOI : https://doi.org/10.5802/tsg.278
Classification:  58C40,  58J53,  30Fxx
Keywords: translation surfaces, flat Laplace operator, isospectrality
@article{TSG_2009-2010__28__51_0,
     author = {Hillairet, Luc},
     title = {Spectral theory of translation surfaces : A short introduction},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     year = {2009-2010},
     pages = {51-62},
     doi = {10.5802/tsg.278},
     language = {en},
     url = {http://www.numdam.org/item/TSG_2009-2010__28__51_0}
}
Hillairet, Luc. Spectral theory of translation surfaces : A short introduction. Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010) , pp. 51-62. doi : 10.5802/tsg.278. http://www.numdam.org/item/TSG_2009-2010__28__51_0/

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