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Conformality and \(Q\)-harmonicity in sub-Riemannian manifolds. (English. French summary) Zbl 1411.53024

Authors’ abstract: We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of \(Q\)-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact sub-Riemannian manifolds. Together with the recent results in [L. Capogna and E. Le Donne, “Conformal equivalence of visual metrics in pseudo-convex domains”, Preprint, arxiv:1703.00238], our work yields a new proof of the smoothness of boundary extensions of biholomorphisms between strictly pseudoconvex smooth domains [C. Fefferman, Invent. Math. 26, 1–65 (1974; Zbl 0289.32012)].

MSC:

53C17 Sub-Riemannian geometry
35H20 Subelliptic equations
58C25 Differentiable maps on manifolds

Citations:

Zbl 0289.32012
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Full Text: DOI arXiv

References:

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