Spectral theory of translation surfaces : A short introduction
Luc Hillairet1
1 Université de Nantes Laboratoire de mathématiques Jean Leray UMR CNRS 6629 2 rue de la Houssinière BP 92208 44322 Nantes cedex 3 (France)
Séminaire de théorie spectrale et géométrie, Volume 28 (2009-2010), pp. 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: 10.5802/tsg.278
Classification: 58C40, 58J53, 30Fxx
Keywords: translation surfaces, flat Laplace operator, isospectrality
Luc Hillairet 1

1 Université de Nantes Laboratoire de mathématiques Jean Leray UMR CNRS 6629 2 rue de la Houssinière BP 92208 44322 Nantes cedex 3 (France) 
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Luc Hillairet. 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. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.278/

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