Oka's lemma

Template:Short description Template:For In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in ${ℂ}^n$, the function $-\log d(z)$ is plurisubharmonic, where $d$ 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. Furthermore, Oka's lemma is the inverse of Levi's problem (unramified Riemann domain over ${ℂ}^n$). Perhaps, this is why Oka referred to Levi's problem as "problème inverse de Hartogs", and could explain why Levi's problem is occasionally referred to as Hartogs' Inverse Problem.

References

• Template:Citation
• Template:Citation
• Template:Citation
• Template:Citation
• Template:Citation

Further reading

• Template:Cite journal
• Template:Citation PDF TeX

Template:Analysis-stub