Oka's lemma

For Oka's lemma about coherent sheaves, see Oka coherence theorem.

In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in Cⁿ, the function –log d(z) is plurisubharmonic, where d is the distance to the boundary. This property shows that the domain is pseudoconvex.

References

Oka, Kiyoshi (1953), "Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur", Jap. J. Math., 23: 97–155, MR 0071089

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