Testing holomorphy on curves

Abstract

For a domain $D\subset {\mathbb{C}}^n$ we construct a continuous foliation of $D$ into one real dimensional curves such that any function $f\in C^1(D)$ which can be extended holomorphically into some neighborhood of each curve in the foliation will be holomorphic on $D$.

References in corpus (1)

• Holomorphic functions on subsets of C