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, Tome 28 (2009-2010), pp. 51-62.

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.

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

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, Tome 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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