Conformal Invariants Associated to a Measure: Conformally Covariant Operators

نویسندگان

  • SUN-YUNG A. CHANG
  • MATTHEW J. GURSKY
  • PAUL YANG
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.

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تاریخ انتشار 2009