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On fully nonlinear CR invariant equations on the Heisenberg group. (English) Zbl 1235.32026

In the frame of studying the similarities between conformal geometry and CR geometry, the authors investigate fully nonlinear CR invariant equations of the second order on the Heisenberg group \( \mathbb H^{n}\) (which plays in CR geometry the same role as \( \mathbb R ^{n}\) in conformal geometry, while the Cayley transform corresponds to the stereographic projection). Two comparison principles for solutions of families of fully nonlinear second order operators, one on bounded domains of \( \mathbb H^{n}\), the other one on a punctured ball, are also proved. A very interesting discussion on the subject, preliminary notions and definitions necessary in order to facilitate the understanding of the results and a technical appendix are also presented.

MSC:

32V05 CR structures, CR operators, and generalizations
32V20 Analysis on CR manifolds
32V25 Extension of functions and other analytic objects from CR manifolds
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