Conformal invariants associated to a measure: conformally covariant operators
By adapting the construction of Graham et al. [\textit{C. R. Graham, R. Jenne, L. J. Mason} and \textit{G. A. J. Sparling}, J. Lond. Math. Soc., II. Ser. 46, No.~3, 557--565 (1992; Zbl 0726.53010); \textit{C. R. Graham}, J. Lond. Math. Soc., II. Ser. 46, No.~3, 566--576 (1992; Zbl 0726.53011)] to Riemannian measure spaces, the existence of a one-parameter family of conformally covariant operators is shown. As a byproduct of this construction, a family of scalar curvatures is defined, one of which corresponds to Perelman's scalar curvature function. The variational problem naturally associated to this new family of pairs consisting of a scalar curvature function and a covariant operator is studied.
scientific article; zbMATH DE number 5997955