报告人：魏华影 副教授 （江苏师范大学）

时间：2021年12月8日 15:00

报告方式：腾讯会议号：429-546-048

摘要：We consider the space of chord-arc curves on the plane passing through the infinity with their parametrization f on the real line, and embed this space into the product of the BMO Teichmuller spaces.

The fundamental theorem we prove about this representation is that log f' also gives a biholomorphic homeomorphism into the complex Banach space of BMO functions. Using these two equivalent complex structures,we develop a clear exposition on the analytic dependence of involved mappings between certain subspaces. Especially, we examine the parametrization of a chord-arc curve by using the Riemann mapping and its dependence on the arc-length parametrization. As a consequence, we solve completely a conjecture of Katznelson, Nag, and Sullivan in 1990 by showing that this dependence is not continuous, which is our main result. This is a joint work with Katsuhiko Matsuzaki. 

 报告人简介：魏华影，江苏师范大学数学与统计学院副教授，研究方向为Teichmuller theory. 主持国家自然科学基金青年科学基金和江苏省自然科学基金等项目, 论文发表于Adv. Math，Anal. Math. Phys., Bull. Lond. Math. Soc.，Sci. China Math，Pacific J. Math等国内外权威期刊。