Abstract
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 \({p\in M}\) 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.
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Hermann, A. Generic metrics and the mass endomorphism on spin three-manifolds. Ann Glob Anal Geom 37, 163–171 (2010). https://doi.org/10.1007/s10455-009-9179-3
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DOI: https://doi.org/10.1007/s10455-009-9179-3