Oka's lemma, convexity, and intermediate positivity conditions

TL;DR

This paper presents a new proof of Oka's lemma for smoothly bounded, pseudoconvex domains in complex space and extends the method to other convexity-related boundary conditions.

Contribution

It introduces a novel proof technique for Oka's lemma and applies it to broader convexity-like boundary hypotheses.

Findings

New proof of Oka's lemma for pseudoconvex domains

Extension of proof method to other convexity conditions

Enhanced understanding of boundary convexity in complex analysis

Abstract

A new proof of Oka's lemma is given for smoothly bounded, pseudoconvex domains $D\subset\mathbb{C}^n$. The method of proof is then also applied to other convexity-like hypotheses on the boundary of $D$.