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Nonlinear equations on Carnot groups and curvature problems for CR manifolds

Ermanno Lanconelli (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 C R manifolds. We restrict our presentation to the cases of the Webster-Tanaka curvature problem for the C R sphere and of the Levi-curvature equation for strictly pseudoconvex functions.

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