Geodesic
On Families of Complex Lines Sufficient for Holomorphic Extension
Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 545-551

Voir la notice de l'article provenant de la source Math-Net.Ru

It is shown that the set $\mathfrak L_\Gamma$ of all complex lines passing through a germ of a generating manifold $\Gamma$ is sufficient for any continuous function $f$ defined on the boundary of a bounded domain $D\subset\mathbb C^n$ with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from $\mathfrak L_\Gamma$ to admit a holomorphic extension to $D$ as a function of many complex variables.
Keywords: holomorphic extension property, family of complex lines, Hartogs' theorem, Bochner–Martinelli integral, Sard's theorem
Mots-clés : Cauchy–Riemann condition. 
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     author = {A. M. Kytmanov and S. G. Myslivets},
     title = {On {Families} of {Complex} {Lines} {Sufficient} for {Holomorphic} {Extension}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a6/}
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A. M. Kytmanov; S. G. Myslivets. On Families of Complex Lines Sufficient for Holomorphic Extension. Matematičeskie zametki, Tome 83 (2008) no. 4, pp. 545-551. http://geodesic.mathdoc.fr/item/MZM_2008_83_4_a6/