Geometric function theory

G.M. Khenkin (ed.)

The first contribution describes basic concepts, facts and problems of the modern theory of entire functions of several complex variables. The second contribution deals with analogies of basic Nevanlinna's theorems about the distribution of values in the multidimensional case and various applications. The third contribution is devoted to invariant metrics and volumes and their applications in problems of function theory of several variables. The fourth contribution touches upon various results concerning the rigidity of holomorphic mappings of complex spaces beginnning with classical Liouville's and Picard's theorems. Contribution five presents results concerning extension of holomorphic mappings to the boundaries of domains, and results about correspondence of boundaries and equivalence of domains with respect to biholomorphic mappings. Contribution six dwells on the problem of biholomorphic equivalence of manifolds in this differential geometric aspect. The last contribution reviews applications of multidimensional complex geometry in modern physical theories - supergravitation and supergauge fields. This volume will be useful to complex analysts and physicists. It is rounded off by an extensive bibliography.

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  • I. Entire Functions.- II. Multidimensional Value Distribution Theory.- III. Invariant Metrics.- IV. Finiteness Theorems for Holomorphic Maps.- V. Holomorphic Maps in ? and the Problem of Holomorphic Equivalence.- VI. The Geometry of CR-Manifolds.- VII. Supersymmetry and Complex Geometry.- Author Index.

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書名 Geometric function theory
著作者等 Khenkin, G. M.
Dektyarev, I.M.
Khudaverdyan, O.M.
Lin, V. Ya.
Pinchuk, S.I.
Poletskii, E.A.
Ronkin, L. I.
Roslyi, A.A.
Schwarz, A.S.
Peetre, Jaak
書名別名 Kompleksnyĭ analiz--mnogie peremennye 3
シリーズ名 Encyclopaedia of mathematical sciences
出版元 Springer-Verlag
刊行年月 c1989
版表示 Softcover reprint of the original 1st ed. 1989
ページ数 261 p.
大きさ 24 cm
ISBN 3540170057
NCID BA06653816
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言語 英語
原文言語 ロシア語
出版国 ドイツ