学术活动
Semicontinuity theorems on holomorphic automorphism groups
2011-09-23
来源:科技处 点击次数:主讲人:Prof. Kang-Tae Kim (Pohang University of Science and Technology, 韩国)
时 间: 9月23日(周五)16:00-17:00
地 点:数学科学学院311教室
备 注:Abstract: I will begin (with some preliminary introduction) with the following theorem: If a sequence W(j) of bounded strongly pseudoconvex domains converge to a bounded strongly pseudoconvex domain W, not biholomorphic to the unit ball, then there exists N>0 such that Aut W(j) is Lie isomorphic to a subgroup of Aut W, for every j>N. This is the (upper) semicontinuity phenomenon in the sense that the limit group is "larger" than each Aut W(j). Such a phenomenon is in fact general, and has been observed with rigorous proofs in a veriety of contexts and settings in geometry. This line of study has a deep root. I would like to give a comprehensive introduction on this circle of thoughts and research, with my recent work with Robert E. Greene of U.C.L.A.