Several Complex Variables III: Geometric Function Theory (Encyclopaedia of Mathematical Sciences)

ISBN 10: 3642647855 / ISBN 13: 9783642647857

Edité par Springer, 2011

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N° de réf. du vendeur I-9783642647857

Détails bibliographiques

• Titre: Several Complex Variables III: Geometric Function Theory (Encyclopaedia of Mathematical Sciences)
• Éditeur: Springer
• Date de parution: 2011
• Langue: anglais
• ISBN à 10 chiffres: 3642647855
• ISBN à 13 chiffres: 9783642647857
• Reliure: Couverture souple
• État de l'article: New

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Synopsis

We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Présentation de l'éditeur

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.