报告题目：Uniformly perfect sets, Hausdorff dimension, and conformal capacity

报 告 人：Toshiyuki Sugawa（Tohoku University）

报告时间：2025年4月3日（周四）16:30-18:00

报告地点：理学院五楼数学研究中心报告厅(528)

报告摘要：

In this talk, we give lower estimates of the capacity in a manner similar to the case of continua when the plates are uniformly perfect. Furthermore, we show that validity of some of those estimates characterizes uniform perfectness of the plates. Most of the estimates are quantitative with explicit bounds. We also mention a lower bound of the Hausdorff dimension of uniformly perfect sets.

报告人简介：

Toshiyuki Sugawa，日本Tohoku University信息与科学研究所教授、博士生导师。在复分析理论、黎曼面、Teichmueller空间理论及拟共形理论等领域做出了许多创造性研究成果，在国际著名杂志《Communications on Pure and Applied Mathematics》《Transactions of the American Mathematical Society》《Mathematische Zeitschrift》《Israel Journal of Mathematics》等发表了100余篇的学术论文，由国际著名出版社出版了2部英文专著。有限无限维复分析及其应用国际会议国际顾问委员会副主席；多个数学杂志（《Journal of Analysis》《Arabian Journal of Mathematics》《Banach Journal of Mathematical Analysis》《Bulletin of the Korean Mathematical Society》等）编委。