We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces.

Keywords:

Huber's theorem, length spectrum, isospectral, orbisurfaces Huber's theorem, length spectrum, isospectral, orbisurfaces

MSC Classifications:

58J53, 11F72 show english descriptions Isospectrality
Spectral theory; Selberg trace formula 58J53 - Isospectrality
11F72 - Spectral theory; Selberg trace formula

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