Geodesic
Conformal Powers of the Laplacian via Stereographic Projection
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: conformal Laplacian; stereographic projection. 
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     author = {C. Robin Graham},
     title = {Conformal {Powers} of the {Laplacian} via {Stereographic} {Projection}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a120/}
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C. Robin Graham. Conformal Powers of the Laplacian via Stereographic Projection. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a120/

[1] Branson T., “Sharp inequalities, the functional determinant, and the complementary series”, Trans. Amer. Math. Soc., 347 (1995), 3671–3742 | DOI | MR | Zbl

[2] Fefferman C., Graham C. R., The ambient metric, arXiv:0710.0919

[3] Gover A. R., “Laplacian operators and $Q$-curvature on conformally Einstein manifolds”, Math. Ann., 336 (2006), 311–334 ; math.DG/0506037 | DOI | MR | Zbl

[4] Graham C. R., “Compatibility operators for degenerate elliptic equations on the ball and Heisenberg group”, Math. Z., 187 (1984), 289–304 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[6] Dowker, JS, “Determinants and conformal anomalies of GJMS operators on spheres”, Journal of Physics A-Mathematical and Theoretical, 44:11, 115402 | DOI