On uniqueness and differentiability in the space of Yamabe metrics

Abstract

We prove that generically (positive) Yamabe metrics are unique in their conformal class, and describe some sufficient conditions which imply that a Yamabe metric of locally maximal scalar curvature is an Einstein metric.

9pp. This is a complete rewritting of the previous version on the same topic, with new title. The reasoning for (2.14) in v1 is incorrect, and this estimate remains an open problem