
SIGMA 3 (2007), 121, 4 pages arXiv:0711.4798
http://dx.doi.org/10.3842/SIGMA.2007.121
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson
Conformal Powers of the Laplacian via Stereographic Projection
C. Robin Graham
Department of Mathematics, University of Washington, Box 354350, Seattle, WA 981954350, USA
Received November 17, 2007; Published online December 15, 2007
Abstract
A new derivation is given of Branson's factorization formula for
the conformally invariant operator on the sphere whose principal part is
the kth power of the scalar Laplacian. The derivation deduces Branson's
formula from knowledge of the corresponding conformally invariant operator
on Euclidean space (the kth power of the Euclidean Laplacian) via
conjugation by the stereographic projection mapping.
Key words:
conformal Laplacian; stereographic projection.
pdf (138 kb)
ps (109 kb)
tex (6 kb)
References
 Branson T., Sharp inequalities, the functional
determinant, and the complementary series, Trans. Amer. Math. Soc. 347
(1995), 36713742.
 Fefferman C., Graham C.R., The ambient metric,
arXiv:0710.0919.
 Gover A.R., Laplacian operators and Qcurvature
on conformally Einstein manifolds, Math. Ann. 336 (2006),
311334, math.DG/0506037.
 Graham C.R., Compatibility operators for degenerate
elliptic equations on the ball and Heisenberg group, Math. Z.
187 (1984), 289304.
 Graham C.R., Jenne R., Mason L.J.,
Sparling G.A.J.,
Conformally invariant powers of the Laplacian, I: Existence, J. London Math. Soc. 46 (1992),
557565.

