Hidehiko Yamabe

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

Life

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

Work

Yamabe was one of the mathematicians (next to Leo Zippin, Andrew Gleason, Deane Montgomery ), who solved 5 in the 1950s Hilbert problem. In the original formulation was to show that locally Euclidean groups are Lie groups, which was solved by Zippin, Montgomery, Gleason. The beyond this case related locally compact groups ( without small subgroups ) triggered Yamabe. Initial work in this direction, he published in 1950 when he proved that path-connected subgroups of Lie groups are Lie groups. His main publications are two to work in Princeton in 1953 in the Annals of Mathematics. Later he worked on differential equations ( particularly the heat equation ), and differential geometry. Shortly before his death he also computer accounts from a sub-problem of the four- color problem.

In the differential geometry of the Yamabe problem is named after him there on a smooth compact Riemannian manifold with three or more dimensions, a metric conformally equivalent to one with constant scalar curvature? Yamabe published in 1960 a purported proof, which, however, turned out to be defective ( Neil Trudinger 1968). The problem was finally resolved by Thierry Aubin and Richard Schoen 1984 ( in a positive sense). After Yamabe Yamabe invariant of the ( explicitly introduced in 1989 by O. Kobayashi and Richard Schoen ) and the Yamabe flow are ( Richard Hamilton) named in differential geometry.

In his memory a Yamabe Symposium has been held since 1989 at the University of Minnesota and Northwestern University.