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).
Publié le : 2002-07-05
Classification:
Smooth hypersurfaces of the complex projective space,
holomorphic extension of CR functions,
jump formula,
global minimality,
one-sided neighborhood,
32V25, 32V10, 32V15, 32D15,
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
@article{hal-00003381,
author = {Dwilewicz, Roman and Merker, Joel},
title = {On the Hartogs-Bochner phenomenon for CR functions in P\_2(C)},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00003381}
}
Dwilewicz, Roman; Merker, Joel. On the Hartogs-Bochner phenomenon for CR functions in P_2(C). HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003381/