We study Riemannian manifolds (Mn, g) equipped with a smooth measure m. We show that the construction of conformally covariant operators of Graham-Jenne-Mason-Sparling can be adapted to this setting. As a byproduct, we define a family of scalar curvatures, one of which corresponds to Perelman's scalar-curvature function. We also study the variational problem naturally associated to these curvature/operator pairs.
All Science Journal Classification (ASJC) codes
- Conformally invariant operators
- Metric measure spaces