On the Hartogs-Bochner phenomenon for CR functions in P_2(C)

Roman Dwilewicz (1) , Joel Merker (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

Let M be a compact, connected C^2-smooth and globally minimal hypersurface M in P_2(C) which divides the projective space into two connected parts U^{+} and U^{-}. We prove that there exists a side, U^- or U^+, such that every continuous CR function on $M$ extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis (nternat. J. Math. 10 (1999), no. 7, 897--915).

Mots clés: Smooth hypersurfaces of the complex projective space; holomorphic extension of CR functions; jump formula; global minimality; one-sided neighborhood

Domaines: Géométrie différentielle [math.DG]

Roman Dwilewicz, Joel Merker. On the Hartogs-Bochner phenomenon for CR functions in P_2(C). Proceedings of the American Mathematical Society, 2002, 130, pp.1975-1980. ⟨hal-00003381⟩