Masatake Kuranishi Explained
Masatake Kuranishi (倉西 正武 Kuranishi Masatake; July 19, 1924 – June 22, 2021)[1] was a Japanese mathematician who worked on several complex variables, partial differential equations, and differential geometry.
Education and career
Kuranishi received in 1952 his Ph.D. from Nagoya University. He became a lecturer there in 1951, an associate professor in 1952, and a full professor in 1958.[2] From 1955 to 1956 he was a visiting scholar at the Institute for Advanced Study in Princeton, New Jersey.[3] From 1956 to 1961 he was a visiting professor at the University of Chicago, the Massachusetts Institute of Technology, and Princeton University. He became a professor at Columbia University in the summer of 1961.[2]
Kuranishi was an invited speaker at the International Congress of Mathematicians in 1962 at Stockholm with the talk On deformations of compact complex structures[4] and in 1970 at Nice with the talk Convexity conditions related to 1/2 estimate on elliptic complexes. He was a Guggenheim Fellow for the academic year 1975–1976.[5] In 2000 he received the Stefan Bergman Prize.[2] In 2014 he received the Geometry Prize of the Mathematical Society of Japan.
Research
Kuranishi and Élie Cartan established the eponymous Cartan–Kuranishi Theorem on the continuation of exterior differential forms.[6] In 1962, based upon the work of Kunihiko Kodaira and Donald Spencer, Kuranishi constructed locally complete deformations of compact complex manifolds.[7]
In 1982 he made important progress in the embedding problem for CR manifolds (Cauchy–Riemann structures).
Thus, by Kuranishi's work, in real dimension 9 and higher, local embedding of abstract CR structures is true and is also true in real dimension 7 by the work of Akahori.[8] A simplified presentation of Kuranishi's proof is due to Sidney Webster.[9] For
(
i.e., real dimension 3), Nirenberg published a counterexample. The local embedding problem remains open in real dimension 5.
Selected publications
- Heisuke Hironaka (ed.): Masatake Kuranishi - Selected Papers, Springer 2010
- Kuranishi: Deformations of compact complex manifolds, Montreal, Presses de l'Universite de Montreal, 1971, 99 pages.
- Kuranishi: Lectures on involutive systems of partial differential equations, Sociedade de matemática de São Paulo, 1967, 75 pages.
- Kuranishi with notes by M.K. Venkatesha Murthy: Lectures on exterior differential systems, Tata Institute of Fundamental Research, 1962.
See also
External links
Notes and References
- https://www.math.columbia.edu/2021/06/24/in-memoriam-masatake-kuranishi/ In Memoriam – Masatake Kuranishi
- https://www.ams.org/notices/200106/people.pdf Bergman Prize for Kuranishi, Notices AMS
- https://www.ias.edu/people/cos/users/4995 Kuranishi, Masatake | Institute for Advanced Study
- On deformations of compact complex structures. Kuranishi, M.. 1963. Proc. Intern. Congr. Math., Stockholm. 357–359. 2015-11-14. https://web.archive.org/web/20151117032007/http://www.mathunion.org/ICM/ICM1962.1/Main/icm1962.1.0357.0359.ocr.pdf. 2015-11-17. dead.
- http://www.gf.org/fellows/all-fellows/masatake-kuranishi/ John Simon Guggenheim Foundation | Masatake Kuranishi
- Kuranishi. Masatake. On É. Cartan's prolongation theorem of exterior differential systems. American Journal of Mathematics. 79. 1957. 1. 1–47. 10.2307/2372381. 2372381.
- Kuranishi. Masatake. On the locally complete families of complex analytic structures. Annals of Mathematics. 75. 1962. 3. 536–577. 10.2307/1970211. 1970211.
- Akahori, Takao. A New approach to the Local Embedding theorem of CR Structures of
(the local solvability of the operator
in the abstract sense). . 67. 366. 1987. 10.1090/memo/0366. free.
- Webster. Sidney, M.. On the Proof of Kuranishi's Embedding Theorem. . 6. 3. 1989. 183–207. 10.1016/S0294-1449(16)30322-5.
