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Curved Versions of the Ovsienko-Redou Operators
Case, Jeffrey S.
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Case, J.S., Lin, Y., Yuan, W. (2023). Curved Versions of the Ovsienko-Redou Operators. International Mathematics Research Notices, 2023(19), 16904-16929. https://doi.org/10.1093/imrn/rnad053
We construct a family of conformally covariant bidifferential operators on pseudo-Riemannian manifolds. Our construction is analogous to the construction of Graham-Jenne-Mason-Sparling of conformally covariant differential operators via tangential powers of the Laplacian in the Fefferman-Graham ambient space. In fact, we completely classify the tangential bidifferential operators on the ambient space, which are expressed purely in terms of the ambient Laplacian. This gives a curved analogue of the classification, due to Ovsienko-Redou and Clerc, of conformally invariant bidifferential operators on the sphere. As an application, we construct a large class of formally self-adjoint conformally invariant differential operators.
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