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.
[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.
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).
In a series of deep papers published in 1982 [Kur I,[8] II,[9] III[10]], Kuranishi developed the theory of harmonic integrals on strongly pseudoconvex CR structures over small balls along the line developed by D. C. Spencer, C. B. Morrey, J. J. Kohn and Nirenberg.
He considered a strongly pseudoconvex CR structure on a manifold of real dimension
[11]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.