Finnish mathematician (1907?1996)
Lars Valerian Ahlfors
(18 April 1907 ? 11 October 1996) was a Finnish
mathematician
, remembered for his work in the field of
Riemann surfaces
and his textbook on
complex analysis
.
Background
[
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]
Ahlfors was born in
Helsinki, Finland
.
[1]
[2]
His mother, Sieva 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 Lindelof
and
Rolf Nevanlinna
.
[1]
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.
[3]
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
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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
[1]
[2]
(the other was
Jesse Douglas
). In 1935 Ahlfors visited
Harvard University
.
[2]
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
Swiss Federal Institute of Technology at 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;
[1]
[2]
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.
[4]
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)
[5]
and
Conformal invariants
(1973).
He made decisive contributions to
meromorphic
curves,
value distribution theory
,
Riemann surfaces
,
conformal geometry
,
quasiconformal mappings
and other areas during his career.
Personal life
[
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]
In 1933, he married Erna Lehnert, an
Austrian
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.
[1]
[2]
See also
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]
Bibliography
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]
Articles
- Ahlfors, Lars V.
An extension of Schwarz's lemma.
Trans. Amer. Math. Soc. 43 (1938), no. 3, 359?364.
doi:10.2307/1990065
- Ahlfors, Lars; Beurling, Arne.
Conformal invariants and function-theoretic null-sets.
Acta Math. 83 (1950), 101?129.
doi:10.1007/BF02392634
- Beurling, A.; Ahlfors, L.
The boundary correspondence under quasiconformal mappings.
Acta Math. 96 (1956), 125?142.
doi:10.1007/BF02392360
- Ahlfors, Lars;
Bers, Lipman
.
Riemann's mapping theorem for variable metrics.
Ann. of Math. (2) 72 (1960), 385?404.
doi:10.2307/1970141
- Ahlfors, Lars Valerian.
Collected papers. Vol. 1. 1929?1955.
Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhauser, Boston, Mass., 1982. xix+520 pp.
ISBN
3-7643-3075-9
- Ahlfors, Lars Valerian.
Collected papers. Vol. 2. 1954?1979.
Edited with the assistance of Rae Michael Shortt. Contemporary Mathematicians. Birkhauser, Boston, Mass., 1982. xix+515 pp.
ISBN
3-7643-3076-7
Books
- 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.
ISBN
0-07-000657-1
[6]
- 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.
ISBN
978-0-8218-5270-5
- 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.
ISBN
0-8218-3644-7
- Ahlfors, Lars V.
Mobius transformations in several dimensions.
Ordway Professorship Lectures in Mathematics. University of Minnesota, School of Mathematics, Minneapolis, Minn., 1981. ii+150 pp.
- Ahlfors, Lars V.; Sario, Leo.
Riemann surfaces.
Princeton Mathematical Series, No. 26 Princeton University Press, Princeton, N.J. 1960 xi+382 pp.
References
[
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]
- ^
a
b
c
d
e
"Lars V. Ahlfors, Mathematician Who Won First Fields Medal; 89"
.
The Boston Globe
. Boston, MA. October 17, 1996. p. 87
. Retrieved
August 14,
2022
– via
Newspapers.com
.
- ^
a
b
c
d
e
"Lars Ahlfors, Leading Mathematician in Complex Analysis, Dies at 89"
.
The Fresno Bee
. Fresno, CA. October 23, 1996. p. 42
. Retrieved
August 14,
2022
– via
Newspapers.com
.
- ^
Ahlfors, Lars Valerian (2015-12-08).
Analytic Functions
. Princeton University Press.
ISBN
978-1-4008-7670-9
.
- ^
Institute for Advanced Study: A Community of Scholars
- ^
Springer, George
.
"Review of
Riemann surfaces
. By Lars V. Ahlfors and Leo Sario"
(PDF)
.
Bull. Amer. Math. Soc
.
67
(2): 170?171.
doi
:
10.1090/S0002-9904-1961-10548-X
.
- ^
Schaeffer, A. C.
(1953).
"Review:
Complex analysis
. By Lars V. Ahlfors"
(PDF)
.
Bull. Amer. Math. Soc
.
59
(5): 464?467.
doi
:
10.1090/S0002-9904-1953-09722-1
.
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