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We develop the notion of renormalized energy in Cauchy–Riemann (CR) geometry for maps from a strictly pseudoconvex pseudo-Hermitian manifold to a Riemannian manifold. This energy is a CR invariant functional whose critical points, which we call CR-harmonic maps, satisfy a CR covariant partial differential equation. The corresponding operator coincides on functions with the CR Paneitz operator.



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The author was supported in part by the grant ANR-17-CE40-0034 of the French National Research Agency ANR (project CCEM).



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