COMPLEX ANALYSIS BY THE L METHOD

主要研究对象是：复射影空间中的伪凸域。设为D^n中的伪凸区域，边界为C^*光滑。在与n.s obony合著的一篇文章中证明，当n<大于等于bbb2 * ω时，不可能是复超曲面（不一定紧致）的并。这仍然是预印本，但在97年9月提交给了ann . math。我们刚刚根据裁判的意见做了修改。在不久的将来，应该会有更广泛的关于列维平面超曲面的研究，因为通过我们在这类流形上的工作，一个丰富的数学实体变得明显。吉川将Kronecker极限公式推广到更高的维度。

MAIN RESEARCH OBJECT IS : PSEUDOCONVEX DOMAINS IN COMPLEX PRJECTIVE SPACES.Let OMEGA be a pseudoconvex domain in D^n with a C^*-smooth boundary *OMEGA. It was shown in a joint article with N.Sibony that, it n<greater than or equal>2 *OMEGA cannot be the union of (not necessarily compact) complex hypersurfaces. This is still a preprint, but submitted to Ann.Math.sin Sept.'97. We have just did a revision according to the referee's opinion. A work of preliminary nature will appear soon in Nagoya Math.J.There should be in a near future more extensive research on Levi-flat hypersurfaces, because a rich mathematical entity became apparent through our work in this kind of manifolds. Yoshikawa generalized Kronecker's limit formula to higher dimensions.