Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)           Volume 3 (2007)

SIGMA 3 (2007), 121, 4 pages      arXiv:0711.4798      doi: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 98195-4350, 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 k-th power of the scalar Laplacian. The derivation deduces Branson's formula from knowledge of the corresponding conformally invariant operator on Euclidean space (the k-th power of the Euclidean Laplacian) via conjugation by the stereographic projection mapping.

Key words: conformal Laplacian; stereographic projection.

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References

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4. Graham C.R., Compatibility operators for degenerate elliptic equations on the ball and Heisenberg group, Math. Z. 187 (1984), 289-304.
5. 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), 557-565.

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