Oka's lemma

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.


  • Oka, Kiyoshi (1953), "Sur les fonctions analytiques de plusieurs variables. IX. Domaines finis sans point critique intérieur", Jpn. J. Math., 23: 97–155, doi:10.4099/jjm1924.23.0_97, MR 0071089
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