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学术报告四十五:A conformally invariant metric on Riemann surfaces associated with quadratic differentials

来源:数学与统计学院     作者:     时间:2017/12/18 16:34:02  0次

数学与统计学院学术报告[2017] 045

(高水平大学建设系列报告115)

报告题目:A conformally invariant metric on Riemann surfaces associated with quadratic differentials

报告人:Toshiyuki SugawaTohoku University, Japan

时间:2017.12.21(本周四)上午1020-1150

地点:科技楼501会议室

报告摘要:There was the conjecture that the space of integrable holomorphic quadratic differentials on a given hyperbolic Riemann surface R is contained in that of (hyperbolically) bounded holomorphic quadratic differentials on R. Pommerenke gave a counterexample to this conjecture and finally Niebur and Sheingorn in 1977 gave a characterization of such a Riemann surface that this conjecture holds. In order to give a quantitative version of their result, we introduce a conformally invariant metric on R and study it. An extremal problem associated to the metric naturally leads to a reproducing formula of new type.

报告人简介:Professor Sugawa graduated from Kyoto University and is currently working at Tohoku University, Japan. His research interests are complex analysis; especially, geometric function theory, quasiconformal mappings, hyperbolic metric, Teichmuller space, and special functions.

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