TY - JOUR
T1 - Conformal invariants associated to a measure
AU - Chang, Sun Yung A.
AU - Gursky, Matthew J.
AU - Yang, Paul
PY - 2006/2/21
Y1 - 2006/2/21
N2 - In this note, we study some conformal invariants of a Riemannian manifold (Mn, g) equipped with a smooth measure m. In particular, we show that there is a natural definition of the Ricci and scalar curvatures associated to such a space, both of which are conformally invariant. We also adapt the methods of Fefferman and Graham [Fefferman, C. & Graham, C. R. (1985) Astérisque, Numero Hors Serie, 95-116] and Graham, Jenne, Mason, and Sparling [Graham, C. R., Jenne, R., Mason, L. J., & Sparling, G. A. J. (1992) J. London Math. Soc. 46, 557-565] to construct families of conformally covariant operators defined on these spaces. Certain variational problems in this setting are considered, including a generalization of the Einstein-Hilbert action.
AB - In this note, we study some conformal invariants of a Riemannian manifold (Mn, g) equipped with a smooth measure m. In particular, we show that there is a natural definition of the Ricci and scalar curvatures associated to such a space, both of which are conformally invariant. We also adapt the methods of Fefferman and Graham [Fefferman, C. & Graham, C. R. (1985) Astérisque, Numero Hors Serie, 95-116] and Graham, Jenne, Mason, and Sparling [Graham, C. R., Jenne, R., Mason, L. J., & Sparling, G. A. J. (1992) J. London Math. Soc. 46, 557-565] to construct families of conformally covariant operators defined on these spaces. Certain variational problems in this setting are considered, including a generalization of the Einstein-Hilbert action.
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U2 - 10.1073/pnas.0510814103
DO - 10.1073/pnas.0510814103
M3 - Article
C2 - 16473942
AN - SCOPUS:33644554483
SN - 0027-8424
VL - 103
SP - 2535
EP - 2540
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 8
ER -