Testing holomorphy on curves

Details Testing holomorphy on curves Testing holomorphy on curves

2010-12-20

arxiv.org/abs/1012.4329v2

Mathematics

Complex Variables

Scientific paper

For a domain $D\subset {\Bbb{C}}^n$ 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 $D$.

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