Conformal invariants associated to a measure: Conformally covariant operators

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

doi:10.2140/pjm.2011.253.37

Conformal invariants associated to a measure: Conformally covariant operators

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	37-56
Number of pages	20
Journal	Pacific Journal of Mathematics
Volume	253
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2011.253.37
State	Published - 2011

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Conformally invariant operators
Metric measure spaces

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10.2140/pjm.2011.253.37

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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.",

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AU - Gursky, Matthew J.

AU - Yang, Paul

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AB - 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.

KW - Conformally invariant operators

KW - Metric measure spaces

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JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -

Conformal invariants associated to a measure: Conformally covariant operators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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