COMPLEX ANALYSIS BY THE L METHOD

主要研究目标：复射影空间中的伪凸域设Ω是D^n中具有C^*-光滑边界 * Ω的伪凸域。在与N.Sibony的一篇联合文章中表明，它n <greater than or equal>2 * Ω不可能是（不一定是紧的）复杂超曲面的并集。这仍然是一个预印本，但提交给安。'97.我们刚刚根据裁判的意见做了修改。一项工作的初步性质将很快出现在名古屋数学。J.应该有在不久的将来更广泛的研究列维平坦超曲面，因为丰富的数学实体变得明显，通过我们的工作在这种流形。Yoshikawa将Kronecker极限公式推广到高维。

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.