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Fatou–Bieberbach Domain
In mathematics, a Fatou–Bieberbach domain is a proper subdomain of \mathbb^n, biholomorphically equivalent to \mathbb^n. That is, an open set \Omega \subsetneq \mathbb^n is called a Fatou–Bieberbach domain if there exists a bijective holomorphic function f:\Omega \rightarrow \mathbb^n whose inverse function f^:\mathbb^n \rightarrow \Omega is holomorphic. It is well-known that the inverse f^ can not be polynomial. History As a consequence of the Riemann mapping theorem, there are no Fatou–Bieberbach domains in the case ''n'' = 1. Pierre Fatou and Ludwig Bieberbach Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi. Biography Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate ... first explored such domains in higher dimensions in the 1920s, hence the name given to them later. Since the 1980s, Fatou–Bieberbach domains have again ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
