$\pmb{{\mbf C}^n}$中对应的边界正则性
Boundary regularity of correspondences in $\pmb{{\mbf C}^n}$
摘要：
设$M, M'$是${\mbf C^n}$中的有限型光滑实解析超曲面，$\h f$是定义在$M$一侧的全纯对应（不一定是真的），连续地扩展到$M$，并将$M$映射到$M'$ .证明了$\h f$作为局部真全纯对应必须扩张到$M$上.这是CR图的Diederich-Pinchuk扩展结果的对应版本。
英文摘要：
Let $M, M'$ be smooth, real analytic hypersurfaces of finite type in ${\mbf C^n}$ and $\h f$ a holomorphic correspondence (not necessarily proper) that is defined on one side of $M$, extends continuously up to $M$ and maps $M$ to $M'$. It is shown that $\h f$ must extend across $M$ as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich--Pinchuk extension result for CR maps.
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。
