Compactness of relatively isospectral sets of surfaces via conformal   surgeries
  We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to reduce to the case of surfaces hyperbolic near infinity recently studied by Borthwick and Perry, or to the closed case by Osgood, Phillips and Sarnak if there are only cusps. 
Pierre Albin, Clara L. Aldana and Fr\'ed\'eric Rochon
math.DG math.SP