Kuranishi Masatake

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Kuranishi Masatake ( Japanese 倉 西 正 武 ; born July 19, 1924 in Tokyo , Tokyo Prefecture ) is a Japanese mathematician who deals with complex analysis , partial differential equations, and differential geometry .

Life

Kuranishi received his PhD from Nagoya University in 1952 . There he had been a lecturer from 1951, assistant professor from 1952 and professor from 1958. From 1956 he was in the USA, where he was initially visiting scholar at the University of Chicago , the Massachusetts Institute of Technology and Princeton University . He was a professor at Columbia University since 1961 .

In 1975 he was a Guggenheim Fellow. In 2000 he received the Stefan Bergman Prize. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Convexity conditions related to 1/2 estimate on elliptic complexes ). In 2014 he received the Geometry Prize of the Japanese Mathematical Society .

plant

Kuranishi (and Élie Cartan ) wrote the Cartan-Kuranishi theorem about the continuation of systems of external differential forms.

In 1962, building on the work of Kodaira Kunihiko and Donald Spencer, he constructed locally complete deformations of compact complex manifolds.

In 1982 he made important progress in the embedding problem of abstract CR structures (Cauchy-Riemann structures): he proved the local embedding for nine and more real dimensions of the real hypersurface under the assumption of strong pseudoconvexity. That was expanded to seven dimensions by T. Akahori and others, the case of five dimensions is open.

A 1948 paper by Kuranishi was an important step in the program of solving Hilbert's Fifth Problem .

Fonts

  • Heisuke Hironaka (Editor): Masatake Kuranishi - Selected Papers , Springer 2010
  • Kuranishi: Deformations of compact complex manifolds , Montreal, Presses de l'Universite de Montreal, 1971.

Web links

Individual evidence

  1. ↑ On E. Cartan's prolongation theorem of exterior differential systems , Am. J. Math., Vol. 79, 1957, pp. 1-47
  2. ↑ On the locally complete families of complex analytic structures , Annals of Math., Volume 75, 1962, pp. 536-577
  3. ↑ Strongly pseudo convex CRstructures over small balls , Part 1, Annals of Mathematics, Volume 115, 1982, pp. 451-500, Part 2, Volume 116, 1982, pp. 1-64, Part 3, Volume 116, 1982, p 249-330
  4. ↑ The dimension results from the dimension of a hypersurface in 2n dimensional space. For three dimensions (n ​​= 2) there is a counterexample from Louis Nirenberg
  5. ↑ So Hidehiko Yamabe in his essay (Annals of Mathematics, Volume 58, 1953, p. 351), which was one of the keystones for solving the Hilbert problem.
Japanese name: As is common in Japan, the family name comes before the first name in this article . Thus Kuranishi is the family name, Masatake the first name.
personal data
SURNAME Kuranishi, Masatake
ALTERNATIVE NAMES 倉 西 正 武 (Japanese)
BRIEF DESCRIPTION Japanese mathematician
DATE OF BIRTH July 19, 1924
PLACE OF BIRTH Tokyo , Tokyo Prefecture