We provide regularity results for CR-maps from a real hypersurface in $n$-dimensional complex space to a Levi-degenerate target hypersurface in a $n + 1$-dimensional space. We address both the real-analytic and the smooth case. Our results allow immediate applications to the study of proper holomorphic maps between Bounded Symmetric Domains.

中文翻译：

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共维数$ 1 $到Levi退化超曲面的CR映射的规则性

我们提供了从$ n $维复杂空间中的实际超曲面到$ n + 1 $维空间中的Levi退化目标超曲面的CR映射的正则结果。我们同时处理真实分析和平滑情况。我们的研究结果可将其立即应用于有界对称域之间适当全同图的研究。