Let (M,g) be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point p∈M is called the mass endomorphism in p associated to the metric g due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page