曲线上的全纯性检验

摘要：

对于定义域$D\subset {\Bbb{C}}^n$，我们构造了$D$的一个连续的叶理，使得任何可以全纯延拓到该叶理中每一条曲线的某个邻域的函数$f\in {C^1(D)}$在$D$上全纯.

英文摘要：

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 $D$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。