Envelopes of holomorphy of some tube sets in $\mathbf C^2$ and the monodromy theorem

S. M. Ivashkovich

Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 189-196

Résumé

The author proves that functions holomorphic in a neighborhood of the set $D+i\partial E$, where $D$ and $E$ are domains in $\mathbf R^2$, extend holomorphically to a neighborhood of the set $D_1+iE$, where $D_1$ is a subdomain of $D$. As a corollary he shows that functions analytic along $D+i\gamma$, where $\gamma$ is a curve in $\mathbf R^2$, are single-valued in a neighborhood of $D+i\gamma$ under certain restrictions to the size of $D$ and $\gamma$. Bibliography: 4 titles.