Extensions of holomorphic maps

Abstract

Several generalizations of the big Picard theorem are obtained.We consider holomorphie maps / from X-A into M C Y.Under various assumptions on X, A, and M we show that / can be extended to a holomorphie or meromorphic map of X into Y. in the unit disk D = \z € C| \z\ < li and holomorphie maps /., •••,/, of D into M with f.(0)=p. .and / (a.) = p.. The length ]a| of a is defined by k fe 1 + \a.\ \a\ = V d(0, a) = Y log---1.■.TT, 1 -¡aA ¿■1