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Title: From Cartan to Tanaka: Getting Real in the Complex World
Contributor(s): Ezhov, Vladimir (author); McLaughlin, Ben (author); Schmalz, Gerd  (author)orcid 
Publication Date: 2011
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Abstract: It is well known from undergraduate complex analysis that holomorphic functions of one complex variable are fully determined by their values at the boundary of a complex domain via the Cauchy integral formula. This is the first instance in which students encounter the general principle of complex analysis in one and several variables that the study of holomorphic objects often reduces to the study of their boundary values. The boundaries of complex domains, having odd topological dimension, cannot be complex objects. This motivated the study of the geometry of real hypersurfaces in complex space. In particular, since all established facts about a particular hypersurface carry over to its image via a biholomorphic mapping in the ambient space, it is important to decide which hypersurfaces are equivalent with respect to such mappings - that is, to solve an equivalence problem for real hypersurfaces in a complex space.
Publication Type: Journal Article
Source of Publication: Notices of the American Mathematical Society, 58(1), p. 20-27
Publisher: American Mathematical Society
Place of Publication: United States of America
ISSN: 1088-9477
Field of Research (FOR): 010102 Algebraic and Differential Geometry
010111 Real and Complex Functions (incl Several Variables)
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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