In
mathematics, Oka's lemma, proved by
Kiyoshi Oka
was a Japanese mathematician who did fundamental work in the theory of several complex variables.
Biography
Oka was born in Osaka. He went to Kyoto Imperial University in 1919, turning to mathematics in 1923 and graduating in 1924.
He was in ...
, states that in a
domain of holomorphy
In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists a holomorphic function on this domain which cannot be extended to a bigger domain.
For ...
in
, the function
is
plurisubharmonic, where
is the distance to the boundary. This property shows that the domain is
pseudoconvex. Historically, this lemma was first shown in the Hartogs domain in the case of two variables, also Oka's lemma is the inverse of the Levi's problem (unramified Riemann domain over
). So maybe that's why Oka called Levi's problem as "problème inverse de Hartogs", and the Levi's problem is occasionally called Hartogs' Inverse Problem.
References
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Further reading
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PDFTeX
Theorems in complex analysis
Lemmas in analysis
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