Conformal Invariants Associated to a Measure: Conformally Covariant Operators
نویسندگان
چکیده
In this paper we study Riemannian manifolds (M, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling can be adapted to this setting. As a by-product, 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.
منابع مشابه
Conformal Invariants Associated to a Measure, Ii: Conformally Covariant Operators
In this paper we continue to study Riemannian manifolds (M, g) equipped with a smooth measure m. In particular, we show that the construction of conformally covariant operators due to Graham-Jenne-Mason-Sparling can be adapted to this setting. As a by-product, we define a family of scalar curvatures, one of which corresponds to Perelman’s scalar curvature function. We also study the variational...
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