Positive mass theorem for the Yamabe problem on spin manifolds
by
Bernd Ammann, Emmanuel Humbert
Positive mass theorem for the Yamabe problem on spin manifolds
.pdf
GAFA 15 (2005), 567-576.
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. Using Witten's argument, we give a very short proof of this fact. This simplifies considerably the proof of the Yamabe problem for spin manifolds.
53C21 (Primary), 58E11, 53C27 (Secondary)
Erratum
In the printed version a term in a local development of the Dirac operator
is not complete, a term is missing.
Here is the corrected version: .pdf
Here is the preprint version close to the printed version:
.dvi, .ps,.ps.gz oder .pdf
Keywords
Positive mass theorem, Yamabe problem, spin manifolds
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Bernd Ammann, Emmanuel Humbert,
The Paper was written on 01.04.2003
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