Extension of Holomorphic Functions From One Side of a Hypersurface
Canadian mathematical bulletin, Tome 48 (2005) no. 4, pp. 500-504

Voir la notice de l'article provenant de la source Cambridge University Press

We give a new proof of former results by $\text{G}$ . Zampieri and the author on extension of holomorphic functions from one side $\Omega$ of a real hypersurface $M$ of ${{\mathbb{C}}^{n}}$ in the presence of an analytic disc tangent to $M$ , attached to $\bar{\Omega }$ but not to $M$ . Our method enables us to weaken the regularity assumptions both for the hypersurface and the disc.
DOI : 10.4153/CMB-2005-046-6
Mots-clés : 32D10 32V25, analytic discs, Poisson integral, holomorphic extension
Baracco, Luca. Extension of Holomorphic Functions From One Side of a Hypersurface. Canadian mathematical bulletin, Tome 48 (2005) no. 4, pp. 500-504. doi: 10.4153/CMB-2005-046-6
@article{10_4153_CMB_2005_046_6,
     author = {Baracco, Luca},
     title = {Extension of {Holomorphic} {Functions} {From} {One} {Side} of a {Hypersurface}},
     journal = {Canadian mathematical bulletin},
     pages = {500--504},
     year = {2005},
     volume = {48},
     number = {4},
     doi = {10.4153/CMB-2005-046-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-046-6/}
}
TY  - JOUR
AU  - Baracco, Luca
TI  - Extension of Holomorphic Functions From One Side of a Hypersurface
JO  - Canadian mathematical bulletin
PY  - 2005
SP  - 500
EP  - 504
VL  - 48
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-046-6/
DO  - 10.4153/CMB-2005-046-6
ID  - 10_4153_CMB_2005_046_6
ER  - 
%0 Journal Article
%A Baracco, Luca
%T Extension of Holomorphic Functions From One Side of a Hypersurface
%J Canadian mathematical bulletin
%D 2005
%P 500-504
%V 48
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2005-046-6/
%R 10.4153/CMB-2005-046-6
%F 10_4153_CMB_2005_046_6

[1] [1] Baouendi, M. S., Rothschild, L. P. and Trepreau, J. M., On the geometry of analytic discs attached to real manifolds J. Differential Geom. 39(1994), 379–405. Google Scholar

[2] [2] Baracco, L. and Zampieri, G., Analytic discs attached to half spaces of n and extension of holomorphic functions. J. Math. Sci. Univ. Tokyo 8(2001), 317–327. Google Scholar

[3] [3] Baracco, L. and Zampieri, G., Analytic discs and extension of CR functions. Compositio Math. 127(2001), 289–295. Google Scholar

[4] [4] Boggess, A., CR manifolds and the tangential Cauchy–Riemann complex. Studies in Advanced Mathematics CRC Press, Boca Raton, FL, 1991. Google Scholar

[5] [5] Diederich, K. and Fornaess, J. E., Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions Invent. Math. 39(1977), 129–141. Google Scholar

[6] [6] Hanges, N. and Trèves, F., Propagation of holomorphic extendibility of CR functions. Math. Ann. 263(1983), 157–177. Google Scholar

[7] [7] Manfrin, R., Scalari, A. and Zampieri, G., Propagation along complex curves on a hypersurface. Kyushu J. Math. 52(1997), 15–22. Google Scholar

[8] [8] Trepreau, J M., Sur le prolongement holomorphe des fonctions C-R définies sur une hypersurface réelle de classe C 2 dans ℂ n . Invent Math. 83(1986), 583–592. Google Scholar

[9] [9] Tumanov, A., Extending CR functions on manifolds of finite type to a wedge. Mat. Sb. 136(1988), 128–139. Google Scholar

[10] [10] Tumanov, A., Connections and propagation of analyticity for CR functions. Duke Math. J. 73(1994), 1–24. Google Scholar

[11] [11] Zampieri, G., Extension of holomorphic functions through a hypersurface by tangent analytic discs. Hokkaido Math. J. 32(2003), 487–496. Google Scholar

Cité par Sources :