TY - JOUR
T1 - Conformal invariants associated to a measure
T2 - Conformally covariant operators
AU - Chang, Sun Yung A.
AU - Gursky, Matthew J.
AU - Yang, Paul
PY - 2011
Y1 - 2011
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=84863357362&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84863357362&partnerID=8YFLogxK
U2 - 10.2140/pjm.2011.253.37
DO - 10.2140/pjm.2011.253.37
M3 - Article
AN - SCOPUS:84863357362
SN - 0030-8730
VL - 253
SP - 37
EP - 56
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -