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On the hyperbolic dirichlet to neumann functional in Hn and Sn

On the hyperbolic dirichlet to neumann functional in Hn and Sn

We prove the injectivity of the linearizatíon of the hyperbolíc Dirichlet to Neumann functional in a "small" bounded domain of the hyperbolic space Hn (resp., the sphere Sn) under some suitable transversality condition.