Positive mass theorem for the Yamabe problem on spin manifolds

Details Positive mass theorem for the Yamabe problem on spin manifolds Positive mass theorem for the Yamabe problem on spin manifolds

2003-04-03

arxiv.org/abs/math/0304043v3

GAFA 15 (2005), 567-576

Mathematics

Differential Geometry

A term is missing in Version 2 and the printed version. The term is added in Version 3

Scientific paper

Let $(M,g)$ be a compact connected spin manifold of dimension $n\geq 3$ whose Yamabe invariant is positive. We assume that $(M,g)$ is locally conformally flat or that $n \in \{3,4,5\}$. According to a positive mass theorem of Witten, the constant term in the asymptotic development of the Green's function of the conformal Laplacian is positive if $(M,g)$ is not conformally equivalent to the sphere. In the present article, we will give a proof for this fact which is considerably shorter than previous proofs. Our proof is a modification of Witten's argument, but no analysis on asymtotically flat spaces is needed.

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