Conformal invariants associated to a measure: Conformally covariant operators

Sun Yung A. Chang, Matthew J. Gursky, Paul Yang

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)37-56
Number of pages20
JournalPacific Journal of Mathematics
Volume253
Issue number1
DOIs
StatePublished - 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Conformally invariant operators
  • Metric measure spaces

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