Spectral theory of translation surfaces : A short introduction

Hillairet, Luc

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

Classification : 58C40, 58J53, 30Fxx
Mots clés : translation surfaces, flat Laplace operator, isospectrality

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