Generic metrics and the mass endomorphism on spin three-manifolds

Zusammenfassung

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 is an element of 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.