On the local Nirenberg problem for the $Q$-curvatures

Philippe Delanoë and Frédéric Robert

Vol. 231 (2007), No. 2, 293–304

DOI: 10.2140/pjm.2007.231.293

Abstract

The local image of each conformal $Q$-curvature operator on the sphere admits no scalar constraint, although identities of Kazdan–Warner type hold for its graph.

Keywords

conformal $Q$-curvature, Nirenberg problem, Fredholm theory, Paneitz–Branson operators, local image, Kazdan–Warner identities

Mathematical Subject Classification 2000

Primary: 58J05

Secondary: 53C99

Milestones

Received: 4 May 2006

Accepted: 22 August 2006

Published: 1 June 2007