복소 불변량에 관하여: 자기동형사상군, 불변거리 그리고 쌍단면곡률

Abstract

In this dissertation, we present several new domains that do not admit any complete Kahler metric with negatively pinched bisectional curvature. Moreover, we show the uniform extension of the automorphisms up to the boundary for the strongly pseudoconvex domains with Ck,a boundaries when k>1, an integer and 0<a<1. This allows us to prove that the semicontinuity theorem for holomorphic automorphism groups holds for the class of bounded strongly pseudoconves domains with Ck+2,a boundary.