Masatake Kuranishi (倉西正武 ''Kuranishi Masatake''; July 19, 1924 – June 22, 2021) was a Japanese mathematician who worked on

several complex variables The theory of functions of several complex variables is the branch of mathematics dealing with complex-valued functions. The name of the field dealing with the properties of function of several complex variables is called several complex variable ...

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s, and

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

Education and career

Kuranishi received in 1952 his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

from

Nagoya University , abbreviated to or NU, is a Japanese national research university located in Chikusa-ku, Nagoya. It was the seventh Imperial University in Japan, one of the first five Designated National University and selected as a Top Type university of T ...

. He became a lecturer there in 1951, an associate professor in 1952, and a full professor in 1958.Bergman Prize for Kuranishi, Notices AMS
/ref> From 1955 to 1956 he was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Princeton, New Jersey Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...

. From 1956 to 1961 he was a visiting professor at the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

, the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

, and

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

. He became a professor at

Columbia University Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhatt ...

in the summer of 1961. Kuranishi was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in 1962 at

Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...

with the talk ''On deformations of compact complex structures'' and in 1970 at

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

with the talk ''Convexity conditions related to 1/2 estimate on elliptic complexes''. He was a

Guggenheim Fellow Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

for the academic year 1975–1976. In 2000 he received the Stefan Bergman Prize. In 2014 he received the Geometry Prize of the

Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ja, 日本数学会) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized ...

Research

Kuranishi and

Élie Cartan Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. ...

established the eponymous Cartan–Kuranishi Theorem on the continuation of exterior differential forms. In 1962, based upon the work of

Kunihiko Kodaira was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers. He was awarded a Fields Medal in 1954, being the first Japanese ...

and Donald Spencer, Kuranishi constructed locally complete deformations of compact complex manifolds. In 1982 he made important progress in the embedding problem for

CR manifold In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Form ...

s (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. A simplified presentation of Kuranishi's proof is due to Sidney Webster. For

n = 2

(''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.

References

External links

Conference at Columbia University in honor of Kuranishi's 80th birthday, 2005
* {{DEFAULTSORT:Kuranishi, Masatake 1924 births 2021 deaths 20th-century Japanese mathematicians 21st-century Japanese mathematicians 20th-century American mathematicians 21st-century American mathematicians Differential geometers PDE theorists Nagoya University alumni Academic staff of Nagoya University Columbia University faculty People from Tokyo Japanese emigrants to the United States Institute for Advanced Study visiting scholars

Education and career

Research

Selected publications

See also

References

External links