Theorems in complex analysis | Lemmas in analysis

Oka's lemma

In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy 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 Levi's problem (unramified Riemann domain ). Therefore, Oka himself calls Levi's problem "problème inverse de Hartogs", and Levi's problem is occasionally called Hartogs' Inverse Problem. (Wikipedia).

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Related pages

Plurisubharmonic function | Mathematics | Pseudoconvexity | Domain of holomorphy | Kiyoshi Oka