Lanconelli: Nonlinear equations on Carnot groups and curvature problems for CR manifolds

Lanconelli, Ermanno:
Nonlinear equations on Carnot groups and curvature problems for CR manifolds
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 14 (2003), fasc. n.3, p. 227-238, (English)
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We give a short overview of sub-Laplacians on Carnot groups starting from a result by Caccioppoli dated 1934. Then we show that sub-Laplacians on Carnot groups of step one arise in studying curvature problems for $CR$ manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the $CR$ sphere and of the Levi-curvature equation for strictly pseudoconvex functions.

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