  The deformation theory of hyperbolic and Euclidean cone-manifolds with all
cone angles less then 2{\pi} plays an important role in many problems in low
dimensional topology and in the geometrization of 3-manifolds. Furthermore,
various old conjectures dating back to Stoker about the moduli of convex
hyperbolic and Euclidean polyhedra can be reduced to the study of deformations
of cone-manifolds by doubling a polyhedron across its faces. This deformation
theory has been understood by Hodgson and Kerckhoff when the singular set has
no vertices, and by Wei{\ss} when the cone angles are less than {\pi}. We prove
here an infinitesimal rigidity result valid for cone angles less than 2{\pi},
stating that infinitesimal deformations which leave the dihedral angles fixed
are trivial in the hyperbolic case, and reduce to some simple deformations in
the Euclidean case. The method is to treat this as a problem concerning the
deformation theory of singular Einstein metrics, and to apply analytic methods
about elliptic operators on stratified spaces. This work is an important
ingredient in the local deformation theory of cone-manifolds by the second
author, see also the concurrent work by Wei{\ss}.
