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Complex Analysis: A Brief Tour into Higher Dimensions

by R. Michael Range

Year of Award: 2004

Publication Information: The American Mathematical Monthly, February 2003, pp. 89-108


This paper provides a tour through some of the foundations of complex analysis in several variables, visiting vantage points from which one can appreciate the fascinating sights that remain hidden if one never ventures beyond the complex plane.  Along the way we encounter some unexpected higher dimensional phenomena and explore fundamental new concepts.

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About the Author: [from The American Mathematical Monthly (2003)]

R. Michael Range earned his Diplom in Mathematik at the University of Göttingen, where lectures of Hans Grauert got him hooked on multidimensional complex analysis. A Fulbright Exchange Fellowship brought him to the United States and UCLA, where he received a Ph.D. in 1971. He has held academic positions at Yale University and at the University of Washington, as well as research positions at institutes in Bonn, Stockholm, Barcelona, and Berkeley. As befits his research interests and his guiding you on a tour to the highlands of complex analysis, Range loves mountains and is an avid downhill skier. A few years ago, inspired and guided by his son, he got into ice climbing and alpine mountaineering. In the pursuit of other means to lift himself above the ground, he recently earned his pilot's certificate


Subject classification(s): Complex Analysis
Publication Date: 
Tuesday, September 23, 2008