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arXiv · 1012.4329

Testing holomorphy on curves

Buma L. Fridman·Daowei Ma
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Abstract

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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Buma L. Fridman, Daowei Ma. 2010-12-20. Testing holomorphy on curves. https://arxiv.org/abs/1012.4329

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