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Conformal powers of the Laplacian via stereographic projection. (English) Zbl 1133.53014

Summary: A new derivation 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 is given. 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.

MSC:

53B20 Local Riemannian geometry
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