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By Ahlfors, Lars Valerian

A regular resource of data of features of 1 complicated variable, this article has retained its vast recognition during this box through being continuously rigorous with no changing into needlessly eager about complex or overspecialized fabric. tough issues were clarified, the ebook has been reviewed for accuracy, and notations and terminology were modernized. bankruptcy 2, complicated services, includes a short part at the switch of size and sector lower than conformal mapping, and masses of bankruptcy eight, Global-Analytic features, has been rewritten so one can introduce readers to the terminology of germs and sheaves whereas nonetheless emphasizing that classical options are the spine of the speculation. bankruptcy four, advanced Integration, now incorporates a new and less complicated evidence of the overall kind of Cauchy's theorem. there's a brief part at the Riemann zeta functionality, exhibiting using residues in a extra fascinating state of affairs than within the computation of sure integrals

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J. 15 (1968), 111-120. , On the continuation of analytic curves, Math. Ann. 184 (1970), 268-274. , On the continuation of analytic sets, Math. Ann. 185 (1970), 1-12. , Nevanlinna defect relations for singular divisors, Invent. Math. 31 (1975), 155-182. , Holomorphic curves in algebraic manifolds, Bull. Amer. Math. Soc. 83 (1977), 553-568. , On holomorphic curves and meromorphic maps in projective spaces, Indiana Univ. Math. J. 28 (1979), 627641. Wilhelm Stoll [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] 33 , Introduction to Carlson-Griffiths equidistribution theory, Lecture Notes in Mathematics, 981 (1983), 64-89, Springer-Verlag.

Serie VIII15 (1979), 93-262. , The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), 89-104. , Meromorphic functions and analytic curves. Annals of Math. Studies 12 Princeton Univ. J. (1943) pp. 269. , Remarks on the first main theorem in equidistribution theory, 7, 77, 777, IV. J. Differential Geometry 2 (1968), 197-202, 369-384, ibid. 3 (1969), 83-94, 433^46. , The equidistribution theory of holomorphic curves. Annals of Math. Studies, 64 Princeton Univ.

In 1991, Ru Min and I [43] [44] [85] proved the conjecture for holomorphic curves and solved the case of the Cartan conjecture for moving targets [46], In 1985, Charles F. Osgood [39] claimed that these theorems are a consequence of his results in diophantine approximation, but to me this implication is not self evident and still has to be established. At the end let me state a result at Notre Dame on this subject matter, combining the work of Emmanuel Bardis [3], and Ru Min and myself [44]. At first some concepts have to be explained.

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