Graham, C.Robin

Conformal powers of the Laplacian via stereographic projection

SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 121, 4 p., electronic only (2007)

Summary

Summary: 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.

Mathematics Subject Classification

53B20

Keywords/Phrases

conformal Laplacian, stereographic projection

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