Lars Valerian Ahlfors (18 April 1907 – 11 October 1996) was a Finnish mathematician, remembered for his work in the field of and his textbook on complex analysis.
Background
Ahlfors was born in Helsinki, Finland.
[ ][ ] His mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a professor of engineering at the Helsinki University of Technology. The Ahlfors family was Swedish-speaking, so he first attended the private school Nya svenska samskolan where all classes were taught in Swedish. Ahlfors studied at University of Helsinki from 1924, graduating in 1928 having studied under Ernst Lindelöf and
Rolf Nevanlinna.
He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an
entire function.
In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem.
It states that the number of asymptotic values approached by an entire function of order ρ along curves in the
complex plane going toward infinity is less than or equal to 2ρ.
He completed his doctorate from the University of Helsinki in 1930.
Career
Ahlfors worked as an associate professor at the University of Helsinki from 1933 to 1936. In 1936 he was one of the first two people to be awarded the
Fields Medal (the other was
Jesse Douglas). In 1935 Ahlfors visited Harvard University.
He returned to
Finland in 1938 to take up a professorship at the University of Helsinki. The outbreak of war in 1939 led to problems although Ahlfors was unfit for military service. He was offered a position at the
ETH Zurich in 1944 and finally managed to travel there in March 1945. He did not enjoy his time in
Switzerland, so in 1946 he jumped at a chance to leave, returning to work at Harvard, where he remained until his retirement in 1977;
he was William Caspar Graustein Professor of Mathematics from 1964. Ahlfors was a visiting scholar at the Institute for Advanced Study in 1962 and again in 1966.
[ Institute for Advanced Study: A Community of Scholars] He was awarded the Wihuri Prize in 1968 and the Wolf Prize in Mathematics in 1981. He served as the Honorary President of the International Congress of Mathematicians in 1986 at Berkeley, California, in celebration of his 50th year of the award of his Fields Medal.
His book Complex Analysis (1953) is the classic text on the subject and is almost certainly referenced in any more recent text which makes heavy use of complex analysis. Ahlfors wrote several other significant books, including Riemann surfaces (1960)
Personal life
In 1933, he married Erna Lehnert, an
Austrians who with her parents had first settled in
Sweden and then in
Finland. The couple had three daughters. Ahlfors died of pneumonia at the Willowwood nursing home in Pittsfield, Massachusetts in 1996.
See also
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Ahlfors finiteness theorem
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Ahlfors function
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Ahlfors measure conjecture
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Beurling–Ahlfors transform
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Schwarz–Ahlfors–Pick theorem
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Measurable Riemann mapping theorem
Bibliography
Articles
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Ahlfors, Lars V. An extension of Schwarz's lemma. Trans. Amer. Math. Soc. 43 (1938), no. 3, 359–364.
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Ahlfors, Lars; Beurling, Arne. Conformal invariants and function-theoretic null-sets. Acta Math. 83 (1950), 101–129.
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Beurling, A.; Ahlfors, L. The boundary correspondence under quasiconformal mappings. Acta Math. 96 (1956), 125–142.
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Ahlfors, Lars; Lipman Bers. Riemann's mapping theorem for variable metrics. Ann. of Math. (2) 72 (1960), 385–404.
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Ahlfors, Lars Valerian. Collected papers. Vol. 1. 1929–1955. Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+520 pp.
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Ahlfors, Lars Valerian. Collected papers. Vol. 2. 1954–1979. Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhäuser, Boston, Mass., 1982. xix+515 pp.
Books
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Ahlfors, Lars V. Complex analysis. An introduction to the theory of analytic functions of one complex variable. Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978. xi+331 pp.
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Ahlfors, Lars V. Conformal invariants. Topics in geometric function theory. Reprint of the 1973 original. With a foreword by Peter Duren, F. W. Gehring and Brad Osgood. AMS Chelsea Publishing, Providence, RI, 2010. xii+162 pp.
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Ahlfors, Lars V. Lectures on quasiconformal mappings. Second edition. With supplemental chapters by C. J. Earle, I. Kra, M. Shishikura and J. H. Hubbard. University Lecture Series, 38. American Mathematical Society, Providence, RI, 2006. viii+162 pp.
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Ahlfors, Lars V. Möbius transformations in several dimensions. Ordway Professorship Lectures in Mathematics. University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. ii+150 pp.
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Ahlfors, Lars V.; Sario, Leo. Riemann surfaces. Princeton Mathematical Series, No. 26 Princeton University Press, Princeton, N.J. 1960 xi+382 pp.
External links
