# 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

Last update of the www-page 3.2.2019