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arxiv: 1012.4329 · v2 · pith:DFZ6CUPOnew · submitted 2010-12-20 · 🧮 math.CV

Testing holomorphy on curves

classification 🧮 math.CV
keywords curvesfoliationconstructcontinuouscurvedimensionaldomainextended
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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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