Hidehiko Yamabe

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Hidehiko Yamabe ( Japanese 山 辺 英 彦 , Yamabe Hidehiko ; born August 22, 1923 in Ashiya , Hyōgo Prefecture ; † November 20, 1960 in Evanston , Illinois ) was a Japanese mathematician .

Life

Yamabe attended Third High School in Tokyo and studied mathematics at Tokyo University from 1944 . After graduating in 1947, he became an assistant at Osaka University . In 1952 he went (shortly after his marriage) to the USA at Princeton University as an assistant to Deane Montgomery . In 1953 he handed from there to Osaka his dissertation and became PhD . In 1954 he was an Assistant Professor at the University of Minnesota and in 1956 an Associate Professor and Sloan Research Fellow . In 1958 he became a professor at Osaka University, but returned to the United States in 1959, where he became a professor at Northwestern University in Evanston in 1960 . He died shortly after of a stroke at the age of 37.

plant

Yamabe was one of the mathematicians (alongside Leo Zippin , Andrew Gleason , Deane Montgomery) who solved Hilbert's 5th problem in the 1950s . The original formulation had to show that locally Euclidean groups are Lie groups, which was solved by Zippin, Montgomery, Gleason. Yamabe solved the further case of connected locally compact groups (without small subgroups ). He published his first work in this direction as early as 1950, when he proved that path-connected subgroups of Lie groups are Lie groups. His main publications are two papers in Princeton 1953 in the Annals of Mathematics. Later he dealt with differential equations (especially the heat conduction equation) and differential geometry. Shortly before his death, he also performed computer calculations on a sub-problem of the four-color problem .

In differential geometry, the Yamabe problem is named after him: on a smooth, compact Riemannian manifold with three or more dimensions, does a metric exist that is conformally equivalent to one with constant scalar curvature? Yamabe published alleged evidence in 1960, but it turned out to be flawed ( Neil Trudinger 1968). The problem was solved by Thierry Aubin and finally Richard Schoen in 1984 (in a positive sense). The Yamabe invariant (introduced explicitly in 1989 by O. Kobayashi and Richard Schoen) and the Yamabe flow ( Richard S. Hamilton ) in differential geometry are named after Yamabe .

A Yamabe symposium has been held in his memory at the University of Minnesota and Northwestern University since 1989.

See also

Web links

Individual evidence

  1. ↑ Preparatory work was also done in 1933 by John von Neumann , who solved the problem in the compact case, Lew Pontryagin , who solved the Abelian case in 1934, Claude Chevalley (who assumed that every locally compact group without a small subgroup is a Lie group ), Masatake Kuranishi ( 1948) and Kenkichi Iwasawa (Annals of Mathematics 1949)
  2. ↑ On an arcwise connected subgroup of a Lie group. In: Osaka Mathematical Journal. Volume 2, 1950, pp. 13-14
  3. ^ On the conjecture of Iwasawa and Gleason. In: Annals of Mathematics. Volume 58, 1953, pp. 48-54, A generalization of a theorem of Gleason. In: Annals of Mathematics. Volume 58, 1953, pp. 351-365
  4. ↑ Yamabe: On a deformation of Riemannian structures on compact manifolds. In: Osaka Journal of Mathematics. Volume 12, 1960, pp. 21-37
  5. ^ Remarks concerning the conformal deformation of Riemannian structures on compact manifolds. In: Ann. Scuola Norm. Sup. Pisa. Volume 22, 1968, pp. 265-274
  6. ↑ In the non-compact case, however, it is wrong, as Jen Zhiren proved in 1988 by giving a counterexample
personal data
SURNAME Yamabe, Hidehiko
ALTERNATIVE NAMES 山 辺 英 彦 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH August 22, 1923
PLACE OF BIRTH Ashiya , Hyogo Prefecture
DATE OF DEATH November 20, 1960
Place of death Evanston , Illinois