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The analytic dilation method was originally used in the context of many bodySchr\"odinger operators. In this paper we adapt it to the context of compatibleLaplacians on complete manifolds with corners of codimension two. As in theoriginal setting of application we show that the method allows us to: First,meromorphically extend the matrix elements associated to analytic vectors.Second, to prove absence of singular spectrum. Third, to find a discrete setthat contains the accumulation points of the pure point spectrum, and finally,it provides a theory of quantum resonances. Apart from these results, we winalso a deeper understanding of the essential spectrum of compatible Laplacianson complete manifolds with corners of codimension 2.

Analytic dilation for Laplacians on manifolds with corners of codimension 2