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Stefan Cohn-Vossen

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Stefan Cohn-Vossen
in Moscow, probably 1936
Born(1902-05-28)28 May 1902
Breslau, Silesia
Died25 June 1936(1936-06-25) (aged 34)
Moscow, Soviet Union
Alma materWrocław University
Known forCohn-Vossen's inequality
Scientific career
FieldsMathematics
ThesisSinguläre Punkte reeller, schlichter Kurvenscharen, deren Differentialgleichung gegeben ist (1924)
Doctoral advisorAdolf Kneser

Stefan Cohn-Vossen (28 May 1902 – 25 June 1936) was a mathematician, specializing in differential geometry. He is best known for his collaboration with David Hilbert on the 1932 book Anschauliche Geometrie, translated into English as Geometry and the Imagination.[1] Both Cohn-Vossen's inequality and the Cohn-Vossen transformation are named after him.[2] He also proved the first version of the splitting theorem.

Biography

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Stefan Cohn-Vossen was born 28 May, 1902 to Emanuel Cohn, a lawyer, and Hedwig (née Vossen) in Breslau (then a city in the Kingdom of Prussia; now Wrocław in Poland). He attended Göttingen in 1920; his notes from Hilbert's lectures on geometry at that time would form the basis for Anschauliche Geometrie. He wrote a 1924 doctoral dissertation at the University of Breslau (now the University of Wrocław) under the supervision of Adolf Kneser.[3] In 1929 he completed his habilitation at Göttingen with his thesis Non-rigid closed surfaces[4] under Richard Courant.[5]

Cohn-Vossen became a professor at the University of Cologne in 1930.[6] In 1931, Cohn-Vossen married Dr. Margot Maria Elfriede Ranft. Anschauliche Geometrie was published in 1932; the book was well reviewed[7][8] and by association with Hilbert, Cohn-Vossen became well known.[9] He was barred from lecturing in 1933 under Nazi racial legislation, because he was Jewish.[10]

Unable to work in Germany, Cohn-Vossen moved to Switzerland in 1934, first to Locarno and then to Zurich, where he taught gymnasium. His son, Richard Cohn-Vossen [de], was born in Zurich in September 1934. Both Courant and Karl Löwner recommended Cohn-Vossen for positions abroad, at Istanbul and Dartmouth respectively; ultimately he emigrated to the USSR, with support from Herman Müntz, Fritz Houtermans, Pavel Alexandrov, and Heinz Hopf,[11] where he was appointed to the Academy of Sciences and worked at Leningrad State University and the Steklov Institute.[12][13]

Cohn-Vossen died in Moscow from pneumonia in 1936.[14] Despite his short time in the USSR, Cohn-Vossen had a significant impact on the development of differential geometry "in the large"[15] in Soviet mathematics.[16][17][18]

Following Cohn-Vossen's death, his widow, Dr. Elfriede Cohn-Vossen, remarried Alfred Kurella, returned to Germany in 1954, and died in 1957. His son, Richard, became a filmmaker. In 1946, unaware of his death, the University of Cologne offered Cohn-Vossen his professorship back.[19]

Publications

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Books

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  • Hilbert, David; Cohn-Vossen, Stefan (1932). Anschauliche Geometrie [Geometry and the Imagination] (in German). Berlin: Springer.
  • Cohn-Vossen, S. E. (Кон-Фоссен С. Э.) (1959). Некоторые вопросы дифференциальной геометрии в целом [Some Problems of Differential Geometry in the Large] (in Russian). Moscow: Fizmatgiz.

Articles

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  • Cohn-Vossen, Stephan (1927). "Singularitäten konvexer Flächen" [Singularities of convex surfaces]. Math. Ann. (in German). 97: 377–386. doi:10.1007/BF01447873.
  • Cohn-Vossen, Stefan (1928). "Die parabolische Kurve. Beitrag zur Geometrie der Berührungstransformationen, der partiellen Differentialgleichung zweiter Ordnung und der Flächenverbiegung". Math. Ann. 99: 273–308. doi:10.1007/BF01459097.
  • Cohn-Vossen, Stefan (1930). "Unstarre geschlossene Flächen" [Non-rigid closed surfaces]. Math. Ann. (in German). 102: 10–29. doi:10.1007/BF01782336.
  • Cohn-Vossen, Stefan (1933). "Sur la courbure totale des surfaces ouvertes". C. R. Acad. Sci. Paris (in French). 197: 1165–1167.
  • Cohn-Vossen, Stefan (1936). "Existenz kürzester Wege" [The existence of shortest paths]. Composito Mathematica (in German). 3: 441–452.
  • Cohn-Vossen, Stephan (1938). "Die Kollineationen desn-dimensionalen Raumes" [Collineations of n-dimensional space]. Math. Ann. (in German). 115: 80–86. doi:10.1007/BF01448928.

See also

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References

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  1. ^ Hilbert, David; Cohn-Vossen, Stephan (1952). Geometry and the Imagination (2nd ed.). Chelsea. ISBN 0-8284-1087-9. {{cite book}}: ISBN / Date incompatibility (help)
  2. ^ Voitsekhovskii, M.I. (2001) [1994], "Cohn-Vossen transformation", Encyclopedia of Mathematics, EMS Press
  3. ^ Stefan Cohn-Vossen at the Mathematics Genealogy Project
  4. ^ Cohn-Vossen 1930.
  5. ^ "Universität zu Köln - Stefan Cohn-Vossen".
  6. ^ Stefan Cohn-Vossen - Erinnerungskolloquium (PDF), Universität zu Köln, 7 November 2014{{citation}}: CS1 maint: location missing publisher (link)
  7. ^ Herbert Turnbull (1933), "Review of Anschauliche Geometrie", Mathematical Gazette, 17 (225): 277–280
  8. ^ "MacTutor - Reviews of David Hilbert's books".
  9. ^ "MacTutor - Stefan Emmanuilovich Cohn-Vossen".
  10. ^ Siegmund-Schultze, Reinhard (2009), Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact, Princeton University Press, pp. 132, 133, 346, 370, 373, 399, ISBN 9780691140414.
  11. ^ Siegmund-Schultze 2009 (p.133) quotes from a 1937 letter by Müntz: "The appointments of Cohn-Vossen, Walfisz, Pollaczek (the latter was not allowed to slip in again) were immediately influenced by myself, the ones for Plessner and Bergmann indirectly."
  12. ^ Pasha Zusmanovich (2024). "Mathematicians going East". Journal of Humanistic Mathematics. 14 (1). arXiv:1805.00242.
  13. ^ Alexandrov, A.D. (1947). "On the works of S.E. Cohn-Vossen". Uspekhi Matematicheskikh Nauk. 3 (19).
  14. ^ Cohn-Vossen's Obituary (in Russian)
  15. ^ "Geometry in the large", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
  16. ^ Alexandrov 1947.
  17. ^ N.V. Efimov (1957). Flachenverbiegung im Grossen. Berlin: Akadamie.
  18. ^ Cohn-Vossen 1959.
  19. ^ Stefan Cohn-Vossen, Erinnerungskolloquium 2014.
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