  100 years ago exactly, in 1906, Hartogs published a celebrated extension
phenomenon (birth of Several Complex Variables), whose global counterpart was
stated in full generality later by Osgood (1929): holomorphic functions in a
connected neighborhood V(bD) of a connected boundary bD contained in C^n (n >=
2) do extend holomorphically and uniquely to the domain D. It was a
long-standing open problem to derive a proof using only analytic discs, as did
Hurwitz (1897), Hartogs (1906) and E.E. Levi (1911) in some special, model
cases. Quite unexpectedly, Fornaess in 1998 exhibited a topologically strange
(nonpseudoconvex) domain D^F in C^2 that cannot be filled in by holomorphic
discs, when one makes the additional requirement that discs must all lie
entirely inside D^F. However, one should point out that the standard,
unrestricted disc method usually allows discs to go outsise the domain (just
think of Levi pseudoconcavity). Confirming these rather ancient expectations,
we show that the global Hartogs extension theorem can be established in such a
natural way.
