关于一类拟凸域的几个性质

Some Properties on a Class of Pseudoconvex Domains

关于一类拟凸域的几个性质①童武（首都师范大学数学系北京１０００３７）本文指出一类拟凸域Ｅ的双全纯不变量ＪＥ（（ｚ，ｗ））在边界Ｅ的点上极限的性质和Ｅ的解析自同胎群的性质．这类拟凸域为Ｅ＝Ｅ（ｍ，ｎ，ｋ）＝｛（ｚ，ｗ）∈Ｃｎ＋ｍ：｜ｚ｜２＋｜ｗ｜２ｋ...

The author proves that the limit for biholomorphic invariant J E((z,w)) on the points of boundary E : lim (z,w)→EJ((z,w))=π n+m (n+m+1) n/(n+m)! when m>1 π n+1 (n+2) n+1 /(n+1)! when m=1 holds on the strongly pseudoconvex points of boundary E ,but not exist on the weakly pseudoconvex points of boundary E . Moreover,the author proves that one can derive same Aut( E ) from any invariant Kahler metric of the domains E .