Ahlfors, Lars Valerian

▪ Finnish mathematician

born April 18, 1907, Helsinki, Fin.

died Oct. 11, 1996, Pittsfield, Mass., U.S.

      Finnish mathematician who was awarded one of the first two Fields Medals in 1936 for his work with Riemann surfaces. He also won the Wolf Prize in 1981.

      Ahlfors received his Ph.D. from the University of Helsinki in 1932. He held an appointment there from 1938 to 1944, then went to the University of Zürich, Switz. He joined the faculty at Harvard University, Cambridge, Mass., U.S., in 1946, remaining there until his retirement.

      Ahlfors was awarded the Fields Medal at the International Congress of Mathematicians in Oslo, Nor., in 1936. He was cited for methods he had developed to analyze Riemann surfaces (Riemann, Bernhard) of inverse functions in terms of covering surfaces. His principal contributions were in the theory of Riemann surfaces, but his theorems (the Ahlfors finiteness theorem, the Ahlfors five-disk theorem, the Ahlfors principal theorem, etc.) touch on other areas as well, such as the theory of finitely generated Kleinian groups. In 1929 he resolved a conjecture of Arnaud Denjoy on entire functions. Later Ahlfors worked on quasi-conformal mappings and, with Arne Beurling, on conformal invariants.

      Ahlfors' publications include Complex Analysis (1953); with Leo Sario, Riemann Surfaces (1960); Lectures on Quasi-Conformal Mappings (1966); and Conformal Invariants (1973). His Collected Papers was published in 1982.

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