Conformal invariants associated to a measure: conformally covariant operators
type: Item
instance of: scholarly article
title: Conformal invariants associated to a measure: conformally covariant operators
zbMATH Open document ID: 1236.53033
author: Matthew J. Gursky
author: Sun-Yung Alice Chang
author: Paul C. Yang
published in: Pacific Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
full work available at URL: p03.xhtml
review text: 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.
reviewed by: Cornelia-Livia Bejan
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 58J05
Mathematics Subject Classification ID: 28C15
zbMATH DE Number: 5997955
zbMATH Keywords: conformally invariant operators
zbMATH Keywords: metric measure spaces
MaRDI profile type: Publication
OpenAlex ID: W2083365020
DOI: 10.2140/PJM.2011.253.37
description: scientific article; zbMATH DE number 5997955